# How do you solve the system of equations 3x - 2y = 1 and 4y=7+3x?

Feb 28, 2017

$x = 3$ and $y = 4$

#### Explanation:

$3 x - 2 y = 1$
$4 y = 7 + 3 x$

From the first equation, determine a temporary value for $3 x$.

$3 x - 2 y = 1$

Add $2 y$ to both sides.

$3 x = 1 + 2 y$

In the second equation, substitute $3 x$ with $\textcolor{red}{\left(1 + 2 y\right)}$.

$4 y = 7 + 3 x$

$4 y = 7 + \textcolor{red}{\left(1 + 2 y\right)}$

Open the brackets and simplify.

$4 y = 7 + 1 + 2 y$

$4 y = 8 + 2 y$

Subtract $2 y$ from both sides.

$2 y = 8$

Divide both sides by $\circ$.

$y = 4$

In the first equation, substitute $y$ with $\textcolor{b l u e}{4}$.

$3 x - 2 y = 1$

$3 x - 2 \left(\textcolor{b l u e}{4}\right) = 1$

Open the brackets and simplify.

$3 x - 8 = 1$

Add $8$ to both sides.

$3 x = 9$

Divide both sides by $3$.

$x = 3$