# What are x and y if 5x - 2y = -5 and y - 5x = 3?

May 9, 2018

color(brown)(x = -1/5, y = 2

#### Explanation:

$5 x - 2 y = - 5 , \text{ Eqn (1)}$

$y - 5 x = 3 , \text{ Eqn (2)}$

$y = 5 x + 3$

Substituting value of y in terms of x in Eqn (1)"#,

$5 x - 2 \cdot \left(5 x + 3\right) = - 5$

$5 x - 10 x - 6 = - 5$

$- 5 x = - 1 , x = - \frac{1}{5}$

$y = 5 x + 3 = 5 \cdot \left(- \frac{1}{5}\right) + 3 = 2$

May 9, 2018

The solution is $\left(- \frac{1}{5} , 2\right)$ or $\left(- 0.2 , 2\right)$.

#### Explanation:

We can also use elimination to solve this system of linear equations.

$\text{Equation 1} :$ $5 x - 2 y = - 5$

$\text{Equation 2} :$ $y - 5 x = 3$

Rewrite Equation 2:

$- 5 x + y = 3$

Add: Equation 1 + Equation 2:

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

Divide both sides by $- 1$. This will reverse the signs.

$y = 2$

Substitute $2$ for $y$ in Equation 2 (either equation will work).

$2 - 5 x = 3$

Subtract $2$ from both sides.

$- 5 x = 3 - 2$

$- 5 x = 1$

Divide both sides by $- 5$.

$x = - \frac{1}{5}$

The solution is $\left(- \frac{1}{5} , 2\right)$ or $\left(- 0.2 , 2\right)$.

graph{(5x-2y+5)(y-5x-3)=0 [-10, 10, -5, 5]}