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

Mar 11, 2018

$x = - 3 \mathmr{and} y = 7$

#### Explanation:

This is one of the best forms you can have for a system of equations. Note that they each have a single $y$ term...

Graphically it means they each represent a straight line and the solution is the point of intersection of the lines.

Write each equation in slope-intercept form, ie with $y$ on one side.

$y = - x + 4 \text{ and } y = - 3 x - 2$

Now, as $y = y$, equate the right sides of the equations:

$- x + 4 = - 3 x - 2$

$3 x - x = - 2 - 4$

$2 x = - 6$

$x = - 3$

Now you can use one equation to find a value for $y$ and the
other equation to check.

$y = - \left(- 3\right) + 4 \text{ "and" } y = - 3 \left(- 3\right) - 2$
$y = 3 + 4 \textcolor{w h i t e}{w w w w w w w w w w w w . w} y = 9 - 2$
$y = 7 \textcolor{w h i t e}{w w w w w w w w w w w w w w w w} y = 7$