# How do you solve by substitution 4x-9y=-21 and 4x+3y=-9?

Jun 8, 2015

$\left(A\right) : 4 x - 9 y = - 21$
$\left(B\right) : 4 x + 3 y = - 9$
We firstly obtain x or y from (A):
$4 x = 9 y - 21$

$x = \frac{9}{4} y - \frac{21}{4}$

And then we put this result at the place of x in (B).

$4 \left(x\right) + 3 y = - 9 \to 4 \left(\frac{9}{4} y - \frac{21}{4}\right) + 3 y = - 9$
$9 y - 21 + 3 y = - 9$
$12 y = 12$
$y = 1$

It is not the end! Now that we found y we have to find x. We can basically substitute y=-5/2 in one of the two equations (for example $\left(A\right)$ ).
$4 x - 9 \left(y\right) = - 21 \to 4 x - 9 \left(1\right) = - 21$
$4 x = - 21 + 9 = - 12$
$x = - 3$

So the solution of the system is $\left(x , y\right) = \left(- 3 , 1\right)$