# How do you solve 2x-4y=4 and x + 4y = 14?

Jul 18, 2017

See a solution process below:

#### Explanation:

Step 1) Solve the second equation for $x$:

$x + 4 y = 14$

$x + 4 y - \textcolor{red}{4 y} = 14 - \textcolor{red}{4 y}$

$x + 0 = 14 - 4 y$

$x = 14 - 4 y$

Step 2) Substitute $\left(14 - 4 y\right)$ for $x$ in the first equation and solve for $y$:

$2 x - 4 y = 4$ becomes:

$2 \left(14 - 4 y\right) - 4 y = 4$

$\left(2 \cdot 14\right) - \left(2 \cdot 4 y\right) - 4 y = 4$

$28 - 8 y - 4 y = 4$

$28 + \left(- 8 - 4\right) y = 4$

$28 + \left(- 12\right) y = 4$

$28 - 12 y = 4$

$- \textcolor{red}{28} + 28 - 12 y = - \textcolor{red}{28} + 4$

$0 - 12 y = - 24$

$- 12 y = - 24$

$\frac{- 12 y}{\textcolor{red}{- 12}} = \frac{- 24}{\textcolor{red}{- 12}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 12}}} y}{\cancel{\textcolor{red}{- 12}}} = 2$

$y = 2$

Step 3) Substitute $2$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = 14 - 4 y$ becomes:

$x = 14 - \left(4 \cdot 2\right)$

$x = 14 - 8$

$x = 6$

The Solution is: $x = 6$ and $y = 2$ or $\left(6 , 2\right)$

Jul 18, 2017

See below

$x = 6 \text{ } y = 2$

#### Explanation:

To solve 2x−4y=4 and $x + 4 y = 14$ , Add the two together

" "2x−4y=4
$\text{ } x + 4 y = 14$

$3 x = 18 \text{ } x = 6$

substitute this into one of the equations

$x + 4 y = 14 \text{ } 6 + 4 y = 14$

$4 y = 8 \text{ } y = 2$