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:

$x - 5 y = 9 \Rightarrow x = 9 + 5 y$ $x-5y=9 rArr color(blue)(x=9+5y$

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

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

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

$- 13 y = 26 \Rightarrow y = - 2$ $-13y=26 rArr color(red)(y=-2)$

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

$x = 9 + 5 (- 2) \Rightarrow x = 9 - 10 \Rightarrow x = - 1$ $x=9+5(color(red)(-2)) rArr x=9-10 rArr color(green)(x=-1)$