# How do you solve y=3x+2 and y=4/3x-5 using substitution?

Dec 23, 2016

$x = - 4 \frac{1}{5}$ and $y = - 10 \frac{3}{5}$

#### Explanation:

$y = 3 x + 2$
$y = \frac{4}{3} x - 5$

In the second equation, substitute $y$ with $\textcolor{red}{\left(3 x + 2\right)}$. This equivalence is taken from the first equation.

$\textcolor{red}{3 x + 2} = \frac{4}{3} x - 5$

Multiply all terms by $3$.

$9 x + 6 = 4 x - 15$

Subtract $4 x$ from each side.

$5 x + 6 = - 15$

Subtract $6$ from each side.

$5 x = - 21$

Divide both sides by $5$.

$x = - \frac{21}{5}$ or $x = - 4 \frac{1}{5}$

In the first equation, substitute $x$ with $\textcolor{b l u e}{- \frac{21}{5}}$.

$y = 3 x + 2$

$y = 3 \textcolor{b l u e}{\left(- \frac{21}{5}\right)} + 2$

$y = - \frac{63}{5} + 2$

$y = \frac{- 63 + 10}{5}$

$y = - \frac{53}{5}$ or $y = - 10 \frac{3}{5}$