# How do you solve 9x+9y=27 and -9x+y=43 using substitution?

Jul 18, 2017

We will start with $9 x + 9 y = 27$ and solve it for $x$

$9 x + 9 y = 27 \iff x + y = 3 \iff x = 3 - y$

We then substitude this into $- 9 x + y = 43$

So we get $- 9 x + y = 43 \iff - 9 \left(3 - y\right) + y = 43 \iff$

$- 27 + 9 y + y = 43 \iff 10 y = 70 \iff y = 7$

We know know $y$ so we can find $x$

$x = 3 - y = 3 - 7 = - 4$

So the solution is $\left(- 4 , 7\right)$