# How do you solve 2x-y=4 and 7x+3y=27 using substitution?

Sep 1, 2017

See a solution process below:

#### Explanation:

Step 1) Solve the first equation for $y$:

$2 x - y = 4$

$- \textcolor{red}{2 x} + 2 x - y = - \textcolor{red}{2 x} + 4$

$0 - y = - 2 x + 4$

$- y = - 2 x + 4$

$\textcolor{red}{- 1} \times x - y = \textcolor{red}{- 1} \left(- 2 x + 4\right)$

$y = \left(\textcolor{red}{- 1} \times - 2 x\right) + \left(\textcolor{red}{- 1} \times 4\right)$

$y = 2 x - 4$

Step 2) Substitute $\left(2 x - 4\right)$ for $y$ in the second equation and solve for $x$:

$7 x + 3 y = 27$ becomes:

$7 x + 3 \left(2 x - 4\right) = 27$

$7 x + \left(3 \times 2 x\right) - \left(3 \times 4\right) = 27$

$7 x + 6 x - 12 = 27$

$\left(7 + 6\right) x - 12 = 27$

$13 x - 12 = 27$

$13 x - 12 + \textcolor{red}{12} = 27 + \textcolor{red}{12}$

$13 x - 0 = 39$

$13 x = 39$

$\frac{13 x}{\textcolor{red}{13}} = \frac{39}{\textcolor{red}{13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{13}}} x}{\cancel{\textcolor{red}{13}}} = 3$

$x = 3$

Step 3) Substitute $3$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = 2 x - 4$ becomes:

$y = \left(2 \times 3\right) - 4$

$y = 6 - 4$

$y = 2$

The Solution Is: $x = 3$ and $y = 2$ or $\left(3 , 2\right)$