# How do you solve the following system?: x +2y =5, -4x +y = -3

Jun 29, 2018

See a solution process below:

#### Explanation:

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

$x + 2 y = 5$

$x + 2 y - \textcolor{red}{2 y} = 5 - \textcolor{red}{2 y}$

$x + 0 = 5 - 2 y$

$x = 5 - 2 y$

Step 2) Substitute $\left(5 - 2 y\right)$ for $x$ in the second equation and solve for $y$:

$- 4 x + y = - 3$ becomes:

$- 4 \left(5 - 2 y\right) + y = - 3$

$\left(- 4 \times 5\right) - \left(- 4 \times 2 y\right) + y = - 3$

$- 20 - \left(- 8 y\right) + y = - 3$

$- 20 + 8 y + y = - 3$

$- 20 + 8 y + 1 y = - 3$

$- 20 + \left(8 + 1\right) y = - 3$

$- 20 + 9 y = - 3$

$- 20 + \textcolor{red}{20} + 9 y = - 3 + \textcolor{red}{20}$

$0 + 9 y = 17$

$9 y = 17$

$\frac{9 y}{\textcolor{red}{9}} = \frac{17}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} y}{\cancel{\textcolor{red}{9}}} = \frac{17}{9}$

$y = \frac{17}{9}$

Step 3) Substitute $\frac{17}{9}$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 5 - 2 y$ becomes:

$x = 5 - \left(2 \times \frac{17}{9}\right)$

$x = 5 - \frac{34}{9}$

$x = \left(\frac{9}{9} \times 5\right) - \frac{34}{9}$

$x = \frac{45}{9} - \frac{34}{9}$

$x = \frac{45 - 34}{9}$

$x = \frac{11}{9}$

The Solution Is:

$x = \frac{11}{9}$ and $y = \frac{17}{9}$

Or

$\left(\frac{11}{9} , \frac{17}{9}\right)$