# How do you solve 3y=11-2x and 3x=y-11?

Mar 14, 2018

Doing some linear algebra, you find that x=-2 and y=5

#### Explanation:

Set up both equations so y (and coefficients) is alone on the left-hand side (LHS). The first one is already done for you:

$3 y = 11 - 2 x$
$y = 11 + 3 x$

Multiply the second equation by 3, and then subtract equation 2 from equation 1:

$\left(y = 11 + 3 x\right) \cdot 3 \Rightarrow 3 y = 33 + 9 x$

$3 y = 11 - 2 x$
$-$
$\underline{3 y = 33 + 9 x}$
$0 = - 22 - 11 x$

Solving for x:

$11 x = - 22 \Rightarrow \textcolor{red}{x = - 2}$

Now, pick either starting equation and plug in x to solve for y:

$y = 11 + 3 x \Rightarrow y = 11 + 3 \left(- 2\right)$
$y = 11 - 6 \Rightarrow \textcolor{b l u e}{y = 5}$