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

Mar 13, 2016

$x = 1$
$y = 2$

#### Explanation:

$1$. Start by labelling the equations.

Equation $1$: $\textcolor{\mathmr{and} a n \ge}{y = - 3 x + 5}$

Equation $2$: $\textcolor{b l u e}{5 x - 4 y = - 3}$

$2$. Substitute equation $1$ into equation $2$.

$\textcolor{b l u e}{5 x - 4 y = - 3}$

$\textcolor{b l u e}{5 x - 4 \textcolor{\mathmr{and} a n \ge}{\left(- 3 x + 5\right)} = - 3}$

$3$. Solve for $x$.

$5 x + 12 x - 20 = - 3$

$17 x = 17$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} x = 1 \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$4$. Substitute $\textcolor{red}{x = 1}$ into equation $1$ to find the value of $y$.

$\textcolor{\mathmr{and} a n \ge}{y = - 3 x + 5}$

$\textcolor{\mathmr{and} a n \ge}{y = - 3 \textcolor{red}{\left(1\right)} + 5}$

$5$. Solve.

$y = - 3 + 5$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = 2 \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\therefore$, $x$ is $1$ and $y$ is $2$.