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

Aug 24, 2017

See a solution process below:

#### Explanation:

Step 1) Because the first equation is already solved for $x$ we can substitute $\left(2 y + 7\right)$ for $x$ in the second equation and solve for $y$:

$3 x - 2 y = 3$ becomes:

$3 \left(2 y + 7\right) - 2 y = 3$

$\left(3 \cdot 2 y\right) + \left(3 \cdot 7\right) - 2 y = 3$

$6 y + 21 - 2 y = 3$

$6 y - 2 y + 21 = 3$

$\left(6 - 2\right) y + 21 = 3$

$4 y + 21 = 3$

$4 y + 21 - \textcolor{red}{21} = 3 - \textcolor{red}{21}$

$4 y + 0 = - 18$

$4 y = - 18$

$\frac{4 y}{\textcolor{red}{4}} = - \frac{18}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} y}{\cancel{\textcolor{red}{4}}} = - \frac{18}{4}$

$y = - \frac{9}{2}$

Step 2) Substitute $- \frac{9}{2}$ for $y$ in the first equation and calculate $x$:

$x = 2 y + 7$ becomes:

$x = \left(2 \times - \frac{9}{2}\right) + 7$

$x = \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times - \frac{9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right) + 7$

$x = - 9 + 7$

$x = - 2$

The Solution Is: $x = - 2$ and $y = - \frac{9}{2}$ or $\left(- 2 , - \frac{9}{2}\right)$