# How do you find x and y? I keep doing guess and check and it takes a long time. please tell me any shortcuts, if you have any. Thanks!

## 3x+2y=7 2x+3y=8

Feb 6, 2018

You can use elimination or substitution to solve this. I will show you elimination because I prefer it. Someone else can do substitution. (Besides, this message is long enough already >_<).

Elimination:
We want to make either $x$ or $y$ have the same coefficient. Let's use $x$:
$3 x + 2 y = 7$
$2 x + 3 y = 8$

$2 \left(3 x + 2 y\right) = 2 \left(7\right)$
$3 \left(2 x + 3 y\right) = 3 \left(8\right)$

$6 x + 4 y = 14$
$6 x + 9 y = 24$

Now subtract the equations. I will subtract the second equation from the first so we don't get negative numbers (no one wants negative numbers if they can avoid them!):

$6 x + 9 y = 24$
$6 x + 4 y = 14$
$-$
$5 y = 10$
$y = 2$
Now substitute for $y$ in one of the equations:
$2 x + 3 \left(2\right) = 8$

$2 x + 6 = 8$

$2 x = 2$
$x = 1$

Checking our answer using the OTHER equation (very important so you don't make the same mistake twice!):
$3 \left(1\right) + 2 \left(2\right) = 7$

$3 + 4 = 7$
$7 = 7$
We're good!
$x = 1 , y = 2$