# How do you solve the following system?: x +7y = 3 , 12x -9 y = 2

Jun 25, 2018

See a solution process below:

#### Explanation:

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

$x + 7 y = 3$

$x + 7 y - \textcolor{red}{7 y} = 3 - \textcolor{red}{7 y}$

$x + 0 = 3 - 7 y$

$x = 3 - 7 y$

Step 2) Substitute $\left(3 - 7 y\right)$ for $x$ in the second equation and solve for $y$:

$12 x - 9 y = 2$ becomes:

$12 \left(3 - 7 y\right) - 9 y = 2$

$\left(12 \times 3\right) - \left(12 \times 7 y\right) - 9 y = 2$

$36 - 84 y - 9 y = 2$

$36 + \left(- 84 - 9\right) y = 2$

$36 + \left(- 93\right) y = 2$

$36 - 93 y = 2$

$36 - \textcolor{red}{36} - 93 y = 2 - \textcolor{red}{36}$

$0 - 93 y = - 34$

$- 93 y = - 34$

$\frac{- 93 y}{\textcolor{red}{- 93}} = - \frac{34}{\textcolor{red}{- 93}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 93}}} y}{\cancel{\textcolor{red}{- 93}}} = \frac{34}{93}$

$y = \frac{34}{93}$

Step 3) Substitute $\frac{34}{93}$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 3 - 7 y$ becomes:

$x = 3 - \left(7 \times \frac{34}{93}\right)$

$x = \left(\frac{93}{93} \times 3\right) - \frac{238}{93}$

$x = \frac{279}{93} - \frac{238}{93}$

$x = \frac{41}{93}$

The Solution Is:

$x = \frac{41}{93}$ and $y = \frac{34}{93}$

Or

$\left(\frac{41}{93} , \frac{34}{93}\right)$