Solve by the linear combination method (with or without multiplication).

2x + 3y = –17
2x + 3y = –17
5x + 2y = –4

(3, –1)
(–2, 2)
(–1, 3)
(2, –7)

Question

Solve by the linear combination method (with or without multiplication).

2x + 3y = –17
2x + 3y = –17
5x + 2y = –4 

       (3, –1)
       (–2, 2)
       (–1, 3)
       (2, –7)

anonymous · Answer

you wrote the first equation twice.$$2x + 3y = –17~~~~~~~->~~~~~~~~\times~~ 2~~~~~~~~~~~~->~~~~~~~~~~~~4x+6y=-34$$$$[5x + 2y = –4~~~~~~~->~~~~~~~\times (-3)~~~~~~~~~~->~~~~~~~~~-15x-6y=12$$

anonymous · Answer

$$add~~~them,~~~you~~~get,~~~~~-11x=-22,~~~~~~~~~x=2$$

anonymous · Answer

once you get the x, it's obvious which of the choices is correct, but you can still solve for y by plugging 2 for x into one of your equations.

anonymous · Answer

$$2(2)+3y=-17$$$$4+3y=-17~~~~~~~~~now,~~~subtract~~~4~~~from~~~both~~~~sides.$$$$4+3y-4=-17-4$$$$3y=-21~~~~~~~~~~~~~~~~~~~~y=-7$$

anonymous · Answer

knowing that according to the first equation if x=2 then y=-7      I'll plug in the values of y and x into the second equation to check.
$$5(2)+2(-7)=-4~~~~~~~~~~->~~~~~~~~~~10+(-14)=-4~~~~~~~-4=-4$$