TIInterActive File Algebra I Unit on Systems of Linear Equations Graphic Method 1) Graph the linear equations y = -x - 2 and y = 2/3 x + 3 2) The intersection of the lines is (___, ____ ) 3) Check the solution algebraically  4) Rewrite these equations in slope intercept form. Graph the equations and find the intersection. 6x - 3y =-15 2 x + y = - 3  5) How many solutions does problem 4 have? a) one b) two c) none d) infinitely many 6) How many solutions exist for these systems? Explain in words your reasoning for this conclusion. 2 x - 3 y = 1 - 2 x + 3 y = 1 1/3 x + y = 2 2 x + 6 y = 12 Substitution Method 7) Solve these multi-step equations for the unknowns. If you need more practice I have a supplement page of equations. a) 10 ( - 4 + y ) = 2 y b) 8 x - 4 ( - 5 x - 2 ) = 12 x 8) Use the substitution method to solve these linear systems. a) x = 8 - 5y - 4 x - 5 y = 7 b) 3 x + 5 y = - 16 - 2 x + 6 y = - 36 c) Explain which problem ( a or b ) is more difficult to solve using the substitution method Explain in words why you made this choice. Linear Elimination Method 9) Simplify these expressions a) - 8 x - 7 - ( - 8 x ) b) 5 y - 11 - ( - 6 ) - 5 y c) What are additive inverses? Give an example and explain what they are in words. 10) To solve this system of equations: a) Rewrite the two equations into standard form. 3 x + 3 y = 8 - 2 y = - 12 + 5 x b) Multiply the equations , if necessary, to get coefficients that are additive inverses for one of the variables. c) Add the equations to eliminate one of the variables and solve for one unknown. d) Substitute the value into one of the equations to solve for the other unknown. e) What is the solution? ( ____, ____ ) f) Explain in words what this solution represents. 11) Solve this system of equations using any method you prefer. You are ordering softballs for two softball leagues. The Pony League uses an 11 inch softball priced at $2.75. The Junior League uses a 12 inch softball priced at $3.25. The bill smeared in the rain, but you know the total was 80 softballs for $245. How many of each size did you order. Define your unknowns. Write two equations from the problem. Solve using the method you prefer. (t @PTimes New Roman.//0>??@z{67_``abccd$%23BCCDRSabbccddexy/00112233445sttuXYYZst$%%&&''(OP  !sttu+,,--..//0pqqr                        dp@ P !$dp@ P !$`'hdhp@ P !$d p@ P !$`'@dd;7 CTxobjItemࡱ> Root Entry{NW` `UContents@OlePres000!  ,,?$@$?$@$?@|4!/l?-DT!@es-8R?-DT!@es-8R? Graph TitleArialXArialYArial?@@$@$$@$$@$$@$ArialCXYFunctionPlotCListBasedPlot??????x CGraphLabel Graph TitleArial XArial YArial,,6U M NANI '@dd;7 CTxobjItemࡱ> Root Entry{NW` `UContents@OlePres000!  ,,?$@$?$@$?@|4!/l?-DT!@es-8R?-DT!@es-8R? Graph TitleArialXArialYArial?@@$@$$@$$@$$@$ArialCXYFunctionPlotCListBasedPlot????L??x CGraphLabel Graph TitleArial XArial YArial,,6U M NANI,XTimes New Roman00/=@{Gz?e