How do you solve –4x + 7y = –10 and x – 5y = 9?

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Answer 1 · 2018-03-14T16:35:59

x=-1, y=-2

Solve for x in one equation, and then substitute x for your solution in the second equation to solve for y, then back-solve for x.

We'll start by solving for x in the second equation, since that is easiest:

#x-5y=9 rArr color(blue)(x=9+5y#

Now that we know x with respect to y, we can use that in the first equation:

#-4color(blue)(x)+7y=-10#

#-4color(blue)((9+5y))+7y=-10 rArr -36-20y+7y=-10#

#-13y=26 rArr color(red)(y=-2)#

Now we know the value of y for this system of equations. Plugging that back into our relation with x:

#x=9+5(color(red)(-2)) rArr x=9-10 rArr color(green)(x=-1)#