• Nqme: :--:-~--------- -- - -- Unit 7 Study Gulde HW standards to be AuessG: MGSE8.EE.8 Analyze and solve pairs of simultaneous linear equations (systems of linear equations). MGSE8.EE.8a Understand that solutions to a system of two linear equations in two variabl es correspond to p oi nts of intersection of their graphs. because points of intersection satisfy both equations simultaneous ly . MGSE8.EE.8b Solve systems of two linear equations in two variables algebraically and estimate solulions by graphing the equations. Solve simple coses by inspection. For example. 3x+2y=5 and 3x+2y=6 have no solution because 3x+2y cannot simultaneously be 5 and 6. MGSE8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For examp le. given coordinates for two pairs of points. determine whether the line through the first pair of point s int ersec ts the line through the second pair. Part A: Solve each system by graphing. Use your ruler. Wr ite your solutions as ordered pairs, where applicable. 1.) y = -x+ 4 y = -x-4 l rr - L - . ,tt - rr---i--- . - f:' I'\. - I - - . .... L'1 ~h __ ._,...L , ii I , r, ,__ ,_ ,- 1-- r-- ' '- I- ,- - - I... L- ,_ ...... - L.. 1- t- " I' I\. I' I - 0 < t, . IL h L:- kl .x I"\. r,.__ .__ 1-- - ,___ '\, r- 1- - r-. w "\ - " 1--t -· - . 1 '- 4 r_..._ - : Solution: -----'--' N,__ S _____ _ 3.) 1 y= --x-3 4 y = x+2 ,\ a}t ' Tq::r -r:r.: , ,-- -·- ~ 7-1 j--f- I .. 0- •·1 i "' r - ,-- 1- t-- --+-- --t- j ,- -+-+-- 1->- ~ . -~ - +· r ,- -• ··, f- . •H , -j - . ,_ _ ., - f- C- L--1-- I/ . -. ,_ . -· I/" '-i- V - -- -· ~ . i,.- i- - b •- .- l· . I· r •--- ... "f) •- ,- . - I! \ I> I [7. I.'\ l D ,-,__ V -+- V ~._ ~- f-- -·' . ' l~ f f "-~ 1-- 1-- - .. r- I .,. r .. - ~-,-- . . . _ ,_ - ; +- - l •n- tt 1 - -j _ f ~~ 1-l--i---- t- .... • i ' - -l - - I 1 •• l i-1 i· j r J t l I ! I ' I J.i_ I 1- LL .J J _.. L ' ' - ff 2.) y=-2x-4 y = x-1 ' -r· .. ::- u~+++t±f+-7 ,-- - '- - •- 7 - -- · i--, . -...... r- :- 1 -:=:- ~ -- j-f - __ .,_'- 1--M - ,- I \ f5 r- L- ~- - - .. .-- -- \ I/ -0 I .k II I/ t· I I l \ / V - _J A -~-- __ ,__ -~f- - . -. J - .... . -- ....i.- ~ - - I ' -l I\ ·- hi-· .. - . ,- . - : .. i· I_, •. ·•i - J / I I Solution: _ __. (~ -- ......., 1 1 _ -_i-+ ) ____ _ 4.) 3 y = -x-2 2 ffitt'T r · -m T .,_ - .. - - j J l,... - I) kl ~.,; . ! 1 ' - "-~ -- .... - , - jj 1. - I . · ·- I I 1 / 1-, f·H f lH- t . . : - ,, +rt tc tr·, - i-. h·-r -- = ---1- ..... ' J....J. l L I i t, Solution: 1 y = -x + 2 2 I = r r ,··· · r- . -- h ; ' I --- - i&' - rn .t -t-r; i· 1 - - .-t-- t,o . 1.,,- ' ..,,; :1 -I ,-..,-... . ·- - :: 1-f~ • .i. --- f jL I o ... .. __. _ .... i-1 I l /t .Lt 1 H· . μ. I T ;- 11 t · t. t ' -~ 1 --! -~- :. I· • j I ti ' I 'i - , '--+ • -, i t. · -' 11 -1 ! " ' I j I ' ' : .. 1. I ! ; I t ~J -+ H 1) L J 1.. . . J 1 , I - I