# How do you solve the following system:  3x – 5y = 53 , 2x + 5y= 2 ?

Jan 31, 2016

Solve by elimination:

$3 x - 5 y = 53$

$2 x + 5 y = 2$

We can eliminate $- 5 y$ in the first equation by $5 y$ in the second equation

$\rightarrow \left(3 x - 5 y = 53\right) + \left(2 x + 5 y = 2\right)$

$\rightarrow = 5 x = 55$

$\rightarrow x = \frac{55}{5} = 11$

Substitute the value of $x$ to the second equation:

$\rightarrow 2 \left(11\right) - 5 y = 2$

$\rightarrow 22 + 5 y = 2$

$\rightarrow + 5 y = 2 - 22$

$\rightarrow + 5 y = - 20$

$\rightarrow y = - \frac{20}{5} = - 4$

So,$\left(x , y\right) = \left(11 , - 4\right)$