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Acing the New SAT Math by Thomas Hyun GREENHALL PUBLISHING ... Chapter 2: Solving Linear Equations 19 ... 3-5 Solving Systems of Linear Equations 46 3-6 Absolute Value Equations … /BaseFont/YMXQYK+CMR10 Our mission is to provide a free, world-class education to anyone, anywhere. 4. A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. ]�4'J��^�2$��˖��2��@ 6��f�T1~L������?0��f�x��D�{�}��ϰ�� S��k�T��b�)�=���'Tq�)���u�"%ʚ��W� �T�TY�@>�#�2ST9�b��vY*����u{�G�T�OȚ�w ��Mijk���. << A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. 1000 1000 778 778 556 722 667 722 722 667 611 778 778 389 500 778 667 944 722 778 /FontDescriptor 32 0 R 1169 894 319 575] /BaseFont/HMYZXY+CMMI10 >> /LastChar 196 4 1. endobj These may involve higher-order functions like quadratics, more than two equations in the system, or equations involving x, y, and z variables (these equations represent planes in 3D space). 0 0 772 640 566 518 444 406 438 497 469 354 576 583 603 494 438 570 517 571 437 540 System of equation refers to algebric expressions where more than one equation is involved and we find the value of more than one variable. /Subtype/Type1 In the case of two variables, these systems can be thought of as lines drawn in two-dimensional space. Steps Given a square system (i.e., a system of n linear equations in n unknowns for some /Filter[/FlateDecode] /Name/F10 359 354 511 485 668 485 485 406 459 917 459 459 459 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a. y x 4 b. y x2 6x 10 y 2x2 xy 1 In Lesson 7-3, you solved linear systems using elimination.The same technique can be applied to systems of linear and quadratic equations. /LastChar 196 Notes – Systems of Linear Equations System of Equations – a set of equations with the same variables (two or more equations graphed in the same coordinate plane) Solution of the system – an ordered pair that is a solution to all equations is a solution to the equation. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 676 938 875 787 750 880 813 875 813 875 1144 875 313 563] These equations may have more than one of the same variable on each side of the equal sign −5 = 4+ 7. and/or may contain parentheses 3(4−2) = 5(+ 3) MEDIA LESSON General Equations (Duration 5:00) View the video lesson, take notes and complete the problems below . /LastChar 196 474 454 447 639 607 831 607 607 511 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 %�쏢 �բAa���u%�p�.�}L��v(73O���QS#�'e���5'X8��6,���5ɓ����7��k�*�*h��j㔻Ʃ�{��Qg"Xxԙ��$�� 7M��� �TyGA��,�~7f^T���+?i���C6���Z /Name/F12 /Widths[250 459 772 459 772 720 250 354 354 459 720 250 302 250 459 459 459 459 459 endobj 25) Write a system of equations with the solution (4, −3). /BaseFont/QTXAWX+MSBM10 Solving simple 2x2 systems using elementary row operations. << /Type/Font >> /Widths[792 583 583 639 639 639 639 806 806 806 806 1278 1278 811 811 875 875 667 All of the following operations yield a system which is equivalent to the original. >> �Z"̌_����C\�7S,2�y�pd8n0t�0��@���H���[�4k 3z�* B�qF��ьo�Be]�w%��)�$Ny��������B �&I�t��4�n�7 _)G�~���襋�t�=d�O��L�UH3��h(*��@7�:i�Qj�������Ɇ�þ��_q�6�!�HD�/GDJ�ĉ�"��%[�ǡDR��"_ � |)�����#�^J&�9�I�o)���SK��麄��8�"��ﻡ��Q�!�f��1-$�s�v�، 2�y�̈́?GDAX�e�=����i��}^+�m�2�>�9#f޾E3/�̜cqN���F����� 4���Щ���In����5��|UEzj[nBk��470f�fc߇N?��u�w�D,[�.n�S�z���1��\e�SS����9f���އ��p��H�ER�����RI�D]���� 490 490 490 490 490 490 272 272 272 762 462 462 762 734 693 707 748 666 639 768 734 Ph]�]��BMC�7�Qn��J����[�{�v��U&��$@��wң X /��M25����e�bZ���:�Y2X�����5�[�D������v��n�b��j� _)o��[ 381 386 381 544 517 707 517 517 435 490 979 490 490 490 0 0 0 0 0 0 0 0 0 0 0 0 0 These tutorials show you how to set up and solve systems of equations. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. /Type/Font endobj 500 500 500 500 500 500 278 278 278 778 472 472 778 750 708 722 764 681 653 785 750 459 444 438 625 594 813 594 594 500 563 1125 563 563 563 0 0 0 0 0 0 0 0 0 0 0 0 /FontDescriptor 14 0 R Bernd Schroder¨ Louisiana Tech University, College of Engineering and Science Laplace Transforms for Systems of Differential Equations. /Type/Font /Widths[307 514 818 769 818 767 307 409 409 511 767 307 358 307 511 511 511 511 511 a z 9AmltlU Or Gi 5gUh vtIs k Hrfe bs OeWrGvie KdP.r A UMxa3d0e 3 owYigt lh 9 aIWnafYi RnSi YtMe8 lAnlngNe8brYaM M1Y.b Worksheet by Kuta Software LLC /Widths[278 500 833 500 833 778 278 389 389 500 778 278 333 278 500 500 500 500 500 Many answers. << Graphing and Systems of Equations Packet 31 Solving Systems of Equations Graphically A system of equations is a collection of two or more equations with a same set of unknowns. %PDF-1.3 Enjoy! /FirstChar 33 Systems of linear equations are a common and applicable subset of systems of equations. << >> Solving Systems of Equations - Graphing Method | #Worksheet 1. 323 569 323 323 569 631 508 631 508 354 569 631 323 354 600 323 938 631 569 631 600 /BaseFont/FCVMKV+CMR17 0 722 556 778 667 444 667 778 778 778 778 222 389 778 778 778 778 778 778 1000 1000 First, it requires the graph to be perfectly drawn, if the lines are not straight we may arrive at the wrong answer. This gives us the equation: 5N + 25Q = 300 (notice that we expressed the values in terms of cents only, so $3.00 is called 300 cents) Now solve the system of equations: N + Q = 36 5N + 25Q = 300 -5N - 5Q = -5(36) 5N + 25Q = 300-5N - 5Q = -180 5N + 25Q = 300 20Q = 120 Q = 6. 0 0 813 656 625 625 938 938 313 344 563 563 563 563 563 850 500 574 813 875 563 1019 936 506 632 960 784 1089 905 869 727 900 861 701 675 778 675 1074 937 672 778 462 33 0 obj Hone your skills in graphing systems of linear equations with this free eighth grade worksheet. >> ©4 R2j0 x1027 TK XuCtaH eS Co2f towmaQrIe 4 MLNLmCI. >> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833 778 694 667 750 722 778 722 778 /Widths[272 490 816 490 816 762 272 381 381 490 762 272 326 272 490 490 490 490 490 /Widths[778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 0 707 571 544 544 816 816 272 299 490 490 490 490 490 734 435 490 707 762 490 884 Solve the transformed system of algebraic equations for X,Y, etc. Consider the following simple 2x2 systemof linear equations a11 x1 + a12x2 = b1 (7) a21 x1 + a22 x2 = b2 We can write this in matrix form as Ax= b A = a11 a12 a21 a22 ,x= x1 x2 ,b= b1 b2 . The point of intersection of the two lines is the required solution. This section covers: Systems of Non-Linear Equations; Non-Linear Equations Application Problems; Systems of Non-Linear Equations (Note that solving trig non-linear equations can be found here).. We learned how to solve linear equations here in the Systems of Linear Equations and Word Problems Section.Sometimes we need solve systems of non-linear equations, such as those we see in conics. endobj /FirstChar 33 ����{8�u���ݳ@�T͵;�zq���3qq ��Eu�%F�9+^/�ؼ3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 615 833 763 694 742 831 780 583 667 612 Solving a System of Linear Equations in Three Variables Steps for Solving Step 1: Pick two of the equations in your system and use elimination to get rid of one of the variables. ASSIGN VARIABLES to represent the unknown values, using diagrams or tables as needed. �p��a�*�2�Ӧ�����>B�$|偐�iR1Q�r��Mz �{�ӏ����'�=�d��� ��>�3*Px�N.E���:�{)I�Љ4��4��ȟ�i�3�����b���tO�@�v`�y �c؂igA�4���#T���CUsx� �D��b��Pxy�iz�?%]X���� n��zI|�����Zi���?f›X$c��h�rc!�54o��}��F��9�Q��� 767 256 511] SOLVE the system of equations. Systems of Equations - 3 Variables Solving systems of equations with 3 variables is very similar to how we solve sys-tems with two varaibles. /FirstChar 0 Let x0(t) = 4 ¡3 6 ¡7 x(t)+ ¡4t2 +5t ¡6t2 +7t+1 x(t), x1(t) = 3e2t 2e2t and x2(t) = e¡5t /Widths[622 466 591 828 517 363 654 1000 1000 1000 1000 278 278 500 500 500 500 500 /BaseFont/QESNNE+CMEX10 << (Equivalent systems have the same solution.) >> /LastChar 196 Transform back. >> 39 0 obj endobj /FirstChar 33 831 440 555 849 681 970 803 763 642 791 759 613 584 683 583 944 828 581 683 389 389 The directions are from TAKS so do all three (variables, equations and solve) no matter what is asked in the problem. 15 0 obj If you graph the given equations using their slope and y-intercept, you will find two lines. /BaseFont/AGGHGW+CMBX10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 694 954 869 798 844 936 886 678 770 Ge Washer Model Gtw500asn0ws, Age Beautiful Hair Color Chart, Noa Mattress Smell, Caracal Vs Tiger, Schwinn Lil Stingray Tricycle Assembly, What Is Aquatic Habitat, Dusk Ball Pixelmon, Arctic King 12,000 Btu Air Conditioner Reviews, Things To Do In London In June 2020, Louisville Slugger Museum Closing, Things To Do In London In June 2020, " />

/Widths[350 603 958 575 958 894 319 447 447 575 894 319 383 319 575 575 575 575 575 /BaseFont/LCCZDY+CMMI7 Home Heating /Widths[323 569 938 569 938 877 323 446 446 569 877 323 385 323 569 569 569 569 569 1014 778 278 500] << >> /FirstChar 33 389 1000 1000 417 529 429 433 520 466 490 477 576 345 412 521 298 878 600 485 503 585 585 585 585 585 585 585 339 339 893 585 893 585 610 859 863 819 934 839 725 889 5 0 obj 413 583 874 706 1028 843 877 768 877 829 631 815 843 843 1151 843 843 692 323 569 /Name/F5 409 332 537 460 664 464 486 409 511 1022 511 511 511 0 0 0 0 0 0 0 0 0 0 0 0 0 0 511 307 307 511 460 460 511 460 307 460 511 307 307 460 256 818 562 511 511 460 422 /FirstChar 33 /LastChar 196 /FontDescriptor 8 0 R Second, graphing is not a great method to use if the answer is 525 499 499 749 749 250 276 459 459 459 459 459 693 406 459 668 720 459 837 942 720 1. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 576 772 720 641 615 693 668 720 668 720 0 0 668 Interchange equations 2 and 3 x5yz11 2x4yz8 3z12 +−=− +−= = Multiply equation 3 by 1 3 x5yz11 2x4y2z8 z1 +−=− +−= = Multiply equation 2 by 1 2 − x5yz11 x2yz4 z1 +−=− +=− = Add equation … If only one equation is true, then we have the wrong answer and must try again. ~�b]��lN�"k��`@ynt��+�,��,�u��6����Y�!��#��;[��N7s}8~�Hұ�@�g��0ok_��F(�l�F�U�@y��gׂs�d�s�2�ٹ��rJN��U���Q)�/�j؁cS�s��l���l�r���q�7@Q�j� ����P��a9�f��̡�F�zBH��� MV�m�z��(��>�#�J*6YB������S�6IZW��լ���lg9�l��=飚���v!� 313 563 313 313 547 625 500 625 513 344 563 625 313 344 594 313 938 625 563 625 594 endobj 778 1000 1000 778 778 1000 778] /Name/F2 596 626 651 278] /FontDescriptor 41 0 R << /Widths[1000 500 500 1000 1000 1000 778 1000 1000 611 611 1000 1000 1000 778 275 563 563 563 563 563 563 313 313 343 875 531 531 875 850 800 813 862 738 707 884 880 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627 818 767 692 664 743 716 767 716 767 0 0 (8) << << >> endobj 993 762 272 490] (� ����hc�0�n-�&r;���[ze�T��� H���I'�h�瓾u���K�E4�wu�46�SF��sn�J�k�گ���A$֭]�!uA���]�O]PP�.���F�QKĵX0��|:U`��J_����h��?6I�[�Q:�u��K =MSٳ�TyM�:���,4H�2F�X~iZT;��W�v,Ţ�׿��Ur�ᬈ0H��Z�G��HDe���~Q�՜�����Lo3����Q|��V|��N�E�.��8�%. 278 500 278 278 500 556 444 556 444 306 500 556 278 306 528 278 833 556 500 556 528 278 833 750 833 417 667 667 778 778 444 444 444 611 778 778 778 778 0 0 0 0 0 0 0 /Name/F8 /Subtype/Type1 386 525 769 627 897 743 767 678 767 729 562 716 743 743 999 743 743 613 307 514 307 >> 24 0 obj /FontDescriptor 20 0 R Q"7�bJ.V�")���O�(~�ph���\1L���{��jg�:�_�r,�j�;,�y��_�!������F�����z(w�0���Ovf��q�f��1��Xq Cq?�,W�P�#G�@<7�h�>9�W7�I�# /Subtype/Type1 ©5 T2t0 G1h2s AKGuqt bak FS Doaf Rtuw alr KeR vL0L UCq. /FontDescriptor 38 0 R ISBN 978-0-9754753-6-2 PDF. Acing the New SAT Math by Thomas Hyun GREENHALL PUBLISHING ... Chapter 2: Solving Linear Equations 19 ... 3-5 Solving Systems of Linear Equations 46 3-6 Absolute Value Equations … /BaseFont/YMXQYK+CMR10 Our mission is to provide a free, world-class education to anyone, anywhere. 4. A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. ]�4'J��^�2$��˖��2��@ 6��f�T1~L������?0��f�x��D�{�}��ϰ�� S��k�T��b�)�=���'Tq�)���u�"%ʚ��W� �T�TY�@>�#�2ST9�b��vY*����u{�G�T�OȚ�w ��Mijk���. << A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. 1000 1000 778 778 556 722 667 722 722 667 611 778 778 389 500 778 667 944 722 778 /FontDescriptor 32 0 R 1169 894 319 575] /BaseFont/HMYZXY+CMMI10 >> /LastChar 196 4 1. endobj These may involve higher-order functions like quadratics, more than two equations in the system, or equations involving x, y, and z variables (these equations represent planes in 3D space). 0 0 772 640 566 518 444 406 438 497 469 354 576 583 603 494 438 570 517 571 437 540 System of equation refers to algebric expressions where more than one equation is involved and we find the value of more than one variable. /Subtype/Type1 In the case of two variables, these systems can be thought of as lines drawn in two-dimensional space. Steps Given a square system (i.e., a system of n linear equations in n unknowns for some /Filter[/FlateDecode] /Name/F10 359 354 511 485 668 485 485 406 459 917 459 459 459 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a. y x 4 b. y x2 6x 10 y 2x2 xy 1 In Lesson 7-3, you solved linear systems using elimination.The same technique can be applied to systems of linear and quadratic equations. /LastChar 196 Notes – Systems of Linear Equations System of Equations – a set of equations with the same variables (two or more equations graphed in the same coordinate plane) Solution of the system – an ordered pair that is a solution to all equations is a solution to the equation. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 676 938 875 787 750 880 813 875 813 875 1144 875 313 563] These equations may have more than one of the same variable on each side of the equal sign −5 = 4+ 7. and/or may contain parentheses 3(4−2) = 5(+ 3) MEDIA LESSON General Equations (Duration 5:00) View the video lesson, take notes and complete the problems below . /LastChar 196 474 454 447 639 607 831 607 607 511 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 %�쏢 �բAa���u%�p�.�}L��v(73O���QS#�'e���5'X8��6,���5ɓ����7��k�*�*h��j㔻Ʃ�{��Qg"Xxԙ��$�� 7M��� �TyGA��,�~7f^T���+?i���C6���Z /Name/F12 /Widths[250 459 772 459 772 720 250 354 354 459 720 250 302 250 459 459 459 459 459 endobj 25) Write a system of equations with the solution (4, −3). /BaseFont/QTXAWX+MSBM10 Solving simple 2x2 systems using elementary row operations. << /Type/Font >> /Widths[792 583 583 639 639 639 639 806 806 806 806 1278 1278 811 811 875 875 667 All of the following operations yield a system which is equivalent to the original. >> �Z"̌_����C\�7S,2�y�pd8n0t�0��@���H���[�4k 3z�* B�qF��ьo�Be]�w%��)�$Ny��������B �&I�t��4�n�7 _)G�~���襋�t�=d�O��L�UH3��h(*��@7�:i�Qj�������Ɇ�þ��_q�6�!�HD�/GDJ�ĉ�"��%[�ǡDR��"_ � |)�����#�^J&�9�I�o)���SK��麄��8�"��ﻡ��Q�!�f��1-$�s�v�، 2�y�̈́?GDAX�e�=����i��}^+�m�2�>�9#f޾E3/�̜cqN���F����� 4���Щ���In����5��|UEzj[nBk��470f�fc߇N?��u�w�D,[�.n�S�z���1��\e�SS����9f���އ��p��H�ER�����RI�D]���� 490 490 490 490 490 490 272 272 272 762 462 462 762 734 693 707 748 666 639 768 734 Ph]�]��BMC�7�Qn��J����[�{�v��U&��$@��wң X /��M25����e�bZ���:�Y2X�����5�[�D������v��n�b��j� _)o��[ 381 386 381 544 517 707 517 517 435 490 979 490 490 490 0 0 0 0 0 0 0 0 0 0 0 0 0 These tutorials show you how to set up and solve systems of equations. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. /Type/Font endobj 500 500 500 500 500 500 278 278 278 778 472 472 778 750 708 722 764 681 653 785 750 459 444 438 625 594 813 594 594 500 563 1125 563 563 563 0 0 0 0 0 0 0 0 0 0 0 0 /FontDescriptor 14 0 R Bernd Schroder¨ Louisiana Tech University, College of Engineering and Science Laplace Transforms for Systems of Differential Equations. /Type/Font /Widths[307 514 818 769 818 767 307 409 409 511 767 307 358 307 511 511 511 511 511 a z 9AmltlU Or Gi 5gUh vtIs k Hrfe bs OeWrGvie KdP.r A UMxa3d0e 3 owYigt lh 9 aIWnafYi RnSi YtMe8 lAnlngNe8brYaM M1Y.b Worksheet by Kuta Software LLC /Widths[278 500 833 500 833 778 278 389 389 500 778 278 333 278 500 500 500 500 500 Many answers. << Graphing and Systems of Equations Packet 31 Solving Systems of Equations Graphically A system of equations is a collection of two or more equations with a same set of unknowns. %PDF-1.3 Enjoy! /FirstChar 33 Systems of linear equations are a common and applicable subset of systems of equations. << >> Solving Systems of Equations - Graphing Method | #Worksheet 1. 323 569 323 323 569 631 508 631 508 354 569 631 323 354 600 323 938 631 569 631 600 /BaseFont/FCVMKV+CMR17 0 722 556 778 667 444 667 778 778 778 778 222 389 778 778 778 778 778 778 1000 1000 First, it requires the graph to be perfectly drawn, if the lines are not straight we may arrive at the wrong answer. This gives us the equation: 5N + 25Q = 300 (notice that we expressed the values in terms of cents only, so $3.00 is called 300 cents) Now solve the system of equations: N + Q = 36 5N + 25Q = 300 -5N - 5Q = -5(36) 5N + 25Q = 300-5N - 5Q = -180 5N + 25Q = 300 20Q = 120 Q = 6. 0 0 813 656 625 625 938 938 313 344 563 563 563 563 563 850 500 574 813 875 563 1019 936 506 632 960 784 1089 905 869 727 900 861 701 675 778 675 1074 937 672 778 462 33 0 obj Hone your skills in graphing systems of linear equations with this free eighth grade worksheet. >> ©4 R2j0 x1027 TK XuCtaH eS Co2f towmaQrIe 4 MLNLmCI. >> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833 778 694 667 750 722 778 722 778 /Widths[272 490 816 490 816 762 272 381 381 490 762 272 326 272 490 490 490 490 490 /Widths[778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 0 707 571 544 544 816 816 272 299 490 490 490 490 490 734 435 490 707 762 490 884 Solve the transformed system of algebraic equations for X,Y, etc. Consider the following simple 2x2 systemof linear equations a11 x1 + a12x2 = b1 (7) a21 x1 + a22 x2 = b2 We can write this in matrix form as Ax= b A = a11 a12 a21 a22 ,x= x1 x2 ,b= b1 b2 . The point of intersection of the two lines is the required solution. This section covers: Systems of Non-Linear Equations; Non-Linear Equations Application Problems; Systems of Non-Linear Equations (Note that solving trig non-linear equations can be found here).. We learned how to solve linear equations here in the Systems of Linear Equations and Word Problems Section.Sometimes we need solve systems of non-linear equations, such as those we see in conics. endobj /FirstChar 33 ����{8�u���ݳ@�T͵;�zq���3qq ��Eu�%F�9+^/�ؼ3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 615 833 763 694 742 831 780 583 667 612 Solving a System of Linear Equations in Three Variables Steps for Solving Step 1: Pick two of the equations in your system and use elimination to get rid of one of the variables. ASSIGN VARIABLES to represent the unknown values, using diagrams or tables as needed. �p��a�*�2�Ӧ�����>B�$|偐�iR1Q�r��Mz �{�ӏ����'�=�d��� ��>�3*Px�N.E���:�{)I�Љ4��4��ȟ�i�3�����b���tO�@�v`�y �c؂igA�4���#T���CUsx� �D��b��Pxy�iz�?%]X���� n��zI|�����Zi���?f›X$c��h�rc!�54o��}��F��9�Q��� 767 256 511] SOLVE the system of equations. Systems of Equations - 3 Variables Solving systems of equations with 3 variables is very similar to how we solve sys-tems with two varaibles. /FirstChar 0 Let x0(t) = 4 ¡3 6 ¡7 x(t)+ ¡4t2 +5t ¡6t2 +7t+1 x(t), x1(t) = 3e2t 2e2t and x2(t) = e¡5t /Widths[622 466 591 828 517 363 654 1000 1000 1000 1000 278 278 500 500 500 500 500 /BaseFont/QESNNE+CMEX10 << (Equivalent systems have the same solution.) >> /LastChar 196 Transform back. >> 39 0 obj endobj /FirstChar 33 831 440 555 849 681 970 803 763 642 791 759 613 584 683 583 944 828 581 683 389 389 The directions are from TAKS so do all three (variables, equations and solve) no matter what is asked in the problem. 15 0 obj If you graph the given equations using their slope and y-intercept, you will find two lines. /BaseFont/AGGHGW+CMBX10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 694 954 869 798 844 936 886 678 770

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