# How do you solve the system of equations by graphing 5x - y =17 and 5x +6y =3?

Jun 27, 2017

See a solution process below:

#### Explanation:

Step 1) Solve each equation for $5 x$:

Equation 1)

$5 x - y = 17$

$5 x - y + \textcolor{red}{y} = 17 + \textcolor{red}{y}$

$5 x - 0 = 17 + y$

$5 x = 17 + y$

Equation 2)

$5 x + 6 y = 3$

$5 x + 6 y - \textcolor{red}{6 y} = 3 - \textcolor{red}{6 y}$

$5 x + 0 = 3 - 6 y$

$5 x = 3 - 6 y$

Step 2) Because the left side of both equations is $5 x$, we can equation the right sides of each equation and solve for $y$:

$17 + y = 3 - 6 y$

$- \textcolor{red}{17} + 17 + 1 y + \textcolor{b l u e}{6 y} = - \textcolor{red}{17} + 3 - 6 y + \textcolor{b l u e}{6 y}$

$0 + \left(1 + \textcolor{b l u e}{6}\right) y = - 14 - 0$

$7 y = - 14$

$\frac{7 y}{\textcolor{red}{7}} = - \frac{14}{\textcolor{red}{7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} y}{\cancel{\textcolor{red}{7}}} = - 2$

$y = - 2$

Step 3) Substitute $- 2$ for $y$ into either of the equations we solved for $5 x$ and calculate $x$. I will choose Equation 1 but either equation can be used:

$5 x = 17 + y$ becomes:

$5 x = 17 + \left(- 2\right)$

$5 x = 17 - 2$

$5 x = 15$

$\frac{5 x}{\textcolor{red}{5}} = \frac{15}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = 3$

$x = 3$

The solution is: $x = 3$ and $y = - 2$ or $\left(3 , - 2\right)$