# How do you solve 3x + 2y = 4 and 2x + y = 3?

Mar 17, 2017

See the entire solution process below:

#### Explanation:

Step 1) Solve the second equation for $y$:

$2 x + y = 3$

$2 x + y - \textcolor{red}{2 x} = 3 - \textcolor{red}{2 x}$

$2 x - \textcolor{red}{2 x} + y = 3 - 2 x$

$0 + y = 3 - 2 x$

$y = 3 - 2 x$

Step 2) Substitute $3 - 2 x$ for $y$ in the first equation and solve for $x$:

$3 x + 2 y = 4$ becomes:

$3 x + 2 \left(3 - 2 x\right) = 4$

$3 x + \left(2 \times 3\right) - \left(2 \times 2 x\right) = 4$

$3 x + 6 - 4 x = 4$

$3 x - 4 x + 6 = 4$

$\left(3 - 4\right) x + 6 = 4$

$- 1 x + 6 = 4$

$- x + 6 - \textcolor{red}{6} = 4 - \textcolor{red}{6}$

$- x + 0 = - 2$

$- x = - 2$

$\textcolor{red}{- 1} \times - x = \textcolor{red}{- 1} \times - 2$

$x = 2$

Step 3) Substitute $2$ for $x$ in the solution to the second equation at the end of Step 1 and calculate $y$:

$y = 3 - 2 x$ becomes:

$y = 3 - \left(2 \times 2\right)$

$y = 3 - 4$

$y = - 1$

The solution is $x = 2$ and $y = - 1$ or $\left(2 , - 1\right)$