# How do you solve 2x + 3y = 2 and x + 6y = 4?

Jun 16, 2018

See a solution process below:

#### Explanation:

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

$x + 6 y = 4$

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

$x + 0 = 4 - 6 y$

$x = 4 - 6 y$

Step 2) Substitute $\left(4 - 6 y\right)$ for $x$ in the first equation and solve for $y$:

$2 x + 3 y = 2$ becomes:

$2 \left(4 - 6 y\right) + 3 y = 2$

$\left(2 \times 4\right) - \left(2 \times 6 y\right) + 3 y = 2$

$8 - 12 y + 3 y = 2$

$8 + \left(- 12 + 3\right) y = 2$

$8 + \left(- 9\right) y = 2$

$8 - 9 y = 2$

$8 - \textcolor{red}{8} - 9 y = 2 - \textcolor{red}{8}$

$0 - 9 y = - 6$

$- 9 y = - 6$

$\frac{- 9 y}{\textcolor{red}{- 9}} = \frac{- 6}{\textcolor{red}{- 9}}$

$y = \frac{2}{3}$

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

$x = 4 - 6 y$ becomes:

$x = 4 - \left(6 \times \frac{2}{3}\right)$

$x = 4 - \frac{12}{3}$

$x = 4 - 4$

$x = 0$

The Solution Is:

$x = 0$ and $y = \frac{2}{3}$

Or

$\left(0 , \frac{2}{3}\right)$