# How do you solve 2(x-4) + y=6 and 3x-2(y-3)=13 using substitution?

Jan 6, 2017

$\left(5 , 4\right)$

#### Explanation:

Substitution means rearranging one of the 2 equations in terms of x or y and substituting into the other equation.

Choosing $2 \left(x - 4\right) + y = 6$ and rearranging to make y the subject.

distribute the bracket.

$2 x - 8 + y = 6$

subtract 2x from both sides.

$\cancel{2 x} \cancel{- 2 x} - 8 + y = 6 - 2 x$

$\cancel{- 8} \cancel{+ 8} + y = 6 + 8 - 2 x$

$\Rightarrow y = 14 - 2 x \leftarrow \textcolor{red}{\text{y is now the subject}}$

We can now substitute this into the other equation and solve for x.

$\Rightarrow 3 x - 2 \left(\textcolor{red}{14 - 2 x} - 3\right) = 13$

$\Rightarrow 3 x - 2 \left(11 - 2 x\right) = 13$

$\Rightarrow 3 x - 22 + 4 x = 13$

$\Rightarrow 7 x = 35 \Rightarrow x = \frac{35}{7} = 5$

We have $y = 14 - 2 x \text{ from above}$ and substituting x = 5 will give corresponding value of y.

$x = 5 \Rightarrow y = 14 - \left(2 \times 5\right) = 14 - 10 = 4$

$\text{Thus solution is } x = 5 , y = 4$

$\textcolor{b l u e}{\text{As a check}}$

2(5-4)+4=2+4=6color(white)(xx)✔︎

"and " (3xx5)-2(4-3)=15-2=13color(white)(xx)✔︎