# How to solve for y in 5x-y=33 and 7x+y=51?

Apr 8, 2015

$y = 5 x - 33$ and $y = - 7 x + 51$.

First Equation:

$5 x - y = 33$

Subtract $5 x$ from both sides.

$- y = 33 - 5 x$

Multiply both sides by $- 1$.

$y = - 33 + 5 x$

Rearrange.

$y = 5 x - 33$

Second Equation:

$7 x + y = 51$

Substitute the $y$ from the first equation

$7 x + \left(5 x - 33\right) = 51 \to 12 x - 33 = 51$

Add $33$ to both sides, and then divide by $12$

$12 x = 84 \to x = 7$

Now put this into the equation for $y$

$y = 5 x - 33 \to y = 5 \cdot 7 - 33 = 35 - 33 \to y = 2$

Answer : $x = 7 , y = 2$