# How to solve this problem?

## 2x+y=3 -2+5y=-9

May 14, 2018

$x = \frac{11}{5} \mathmr{and} y = \frac{- 7}{5}$

#### Explanation:

$2 x + y = 3$
$- 2 + 5 y = - 9$

This is called a system of equations!

To solve this system of equations, we gonna use the substitution method.

So, we wanna solve $5 y - 2 = - 9$ for $y$

$5 y - 2 = - 9$

Start by adding $2$ on both sides

$5 y - 2 + 2 = - 9 + 2$

$5 y = - 7$

Then divide both sides by $5$

$\frac{\cancel{5} y}{\cancel{5}} = \frac{- 7}{5}$

$y = \frac{- 7}{5}$

Now we wanna use the value of $y$ to find the value of $x$.

We gonna do that by substitute $\frac{- 7}{5}$ for $y$ in $2 x + y = 3$
What does that mean? It means that we gonna replace $y$ by $\frac{- 7}{5}$ in the equation.

$2 x + y = 3$

#2x + (-7)/5 = 3

Now we can add $\frac{7}{5}$ to both sides

$2 x + \frac{- 7}{5} + \frac{7}{5} = 3 + \frac{7}{5}$

$2 x = \frac{15 + 7}{5}$

$2 x = \frac{22}{5}$

Divide both sides by $2$

$\frac{\cancel{2} x}{\cancel{2}} = \frac{22}{\frac{5}{2}}$

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

Thus,

The answers are: $x = \frac{11}{5} \mathmr{and} y = \frac{- 7}{5}$