# How do you solve by substitution 5x-6y=6 and 5x+y=2?

Apr 29, 2018

$y = - \frac{4}{7}$
$x = \frac{18}{35}$

#### Explanation:

$5 x - 6 y = 6$ --- (1)
$5 x + y = 2$ --- (2)

(1) minus (2)

$- 6 y - y = 6 - 2$
$- 7 y = 4$
$y = - \frac{4}{7}$ --- (3)

Sub (3) into (1)

$5 x - 6 \times - \frac{4}{7} = 6$
$5 x + \frac{24}{7} = 6$
$5 x = \frac{18}{7}$
$x = \frac{18}{35}$

Apr 29, 2018

The solution is $\left(\frac{18}{35} , - \frac{4}{7}\right)$ or $\left(0.514 , - 0.571\right)$.

#### Explanation:

Solve the system of equations.

$\text{Equation 1} :$ $5 x - 6 y = 6$

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

The solution to the system of linear equations is the point they have in common, the point of intersection. The system will be solved using substitution.

Solve Equation 2 for $y$.

$y = - 5 x + 2$

Substitute $- 5 x + 2$ for $y$ in Equation 1. Solve for $x$.

$5 x - 6 \left(- 5 x + 2\right) = 6$

Expand.

$5 x + 30 x - 12 = 6$

Simplify.

$35 x - 12 = 6$

Add $12$ to both sides.

$35 x = 6 + 12$

Simplify.

$35 x = 18$

Divide both sides by $35$.

$x = \frac{18}{35}$ or $0.514$

Substitute $\frac{18}{35}$ for $x$ in Equation 2. Solve for $y$.

$5 \left(\frac{18}{35}\right) + y = 2$

Simplify ${\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}^{1} \left(\frac{18}{\textcolor{red}{\cancel{\textcolor{b l a c k}{35}}}} ^ 7\right)$ to $\frac{18}{7}$.

$\frac{18}{7} + y = 2$

Multiply both sides by $7$.

${\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}^{1} \times \frac{18}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} ^ 1 + 7 \times y = 2 \times 7$

Simplify.

$18 + 7 y = 14$

Subtract $18$ from both sides.

$7 y = 14 - 18$

Simplify.

$7 y = - 4$

Divide both sides by $7$.

$y = - \frac{4}{7}$ or $- 0.571$

Solution

$\left(\frac{18}{35} , - \frac{4}{7}\right)$ or $\left(0.514 , - 0.571\right)$

graph{(y-5/6x+1)(y+5x-2)=0 [-10, 10, -5, 5]}