Question

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

Answer 1

x=-1, y=-2

Explanation:

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)`