# How do you solve 5x - y = -9 and y + 2x = 2?

Jun 6, 2018

The solution is $\left(- \frac{11}{3} , \frac{28}{3}\right)$ or $\approx \left(- 3.67 , 9.33\right)$.

#### Explanation:

Solve the linear system:

$\text{Equation 1} :$ $5 x - y = - 9$

$\text{Equation 2} :$ $y + 2 x = 2$

I am going to solve the system by elimination and substitution.

Rearrange Equation 2 to standard form: $A x + B y = C$

$2 x - y = 2$

Multiply Equation 2 by $- 1$. This will reverse the signs, but the graph will remain the same.

$- 1 \left(2 x - y\right) = 2 \times - 1$

$- 2 x + y = - 2$

Add Equation 1 and Equation 2.

$\textcolor{w h i t e}{. .} 5 x - y = - 9$
$- 2 x + y = - 2$
$- - - - - - -$
$\textcolor{w h i t e}{. .} 3 x \textcolor{w h i t e}{\ldots . .} = - 11$

Divide both sides by $3$.

$x = - \frac{11}{3}$ or $\approx - 3.67$

Substitute $- \frac{11}{3}$ for $x$ in Equation 2 and solve for $y$.

$2 \left(- \frac{11}{3}\right) + y = 2$

$- \frac{22}{3} + y = 2$

Multiply both sides by $3$.

$- 22 + 3 y = 6$

Add $22$ to both sides.

$3 y = 6 + 22$

Simplify $6 + 22$ to $28$.

$3 y = 28$

Divide both sides by $3$.

$y = \frac{28}{3}$ or $\approx 9.33$

graph{(5x-y+9)(-2x+y+2)=0 [-12.795, 9.705, -15.865, -4.615]}