# How do solve the following linear system?:  3x - y = -6, y = 5x - 7?

Aug 27, 2017

See a solution process below: $\left(\frac{13}{2} , \frac{51}{2}\right)$

#### Explanation:

Step 1) Because the second equation is already solved for $y$ we can substitute $\left(5 x - 7\right)$ for $y$ in the first equation and solve for $x$:

$3 x - y = - 6$ becomes:

$3 x - \left(5 x - 7\right) = - 6$

$3 x - 5 x + 7 = - 6$

$\left(3 - 5\right) x + 7 = - 6$

$- 2 x + 7 = - 6$

$- 2 x + 7 - \textcolor{red}{7} = - 6 - \textcolor{red}{7}$

$- 2 x + 0 = - 13$

$- 2 x = - 13$

$\frac{- 2 x}{\textcolor{red}{- 2}} = \frac{- 13}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} x}{\cancel{\textcolor{red}{- 2}}} = \frac{13}{2}$

$x = \frac{13}{2}$

Step 2) Substitute $\frac{13}{2}$ for $x$ in the second equation and calculate $y$:

$y = 5 x - 7$ becomes:

$y = \left(5 \cdot \frac{13}{2}\right) - 7$

$y = \frac{65}{2} - \left(\frac{2}{2} \times 7\right)$

$y = \frac{65}{2} - \frac{14}{2}$

$y = \frac{51}{2}$

The Solution Is: $x = \frac{13}{2}$ and $y = \frac{51}{2}$ or $\left(\frac{13}{2} , \frac{51}{2}\right)$