# How do you solve the following system of linear equations by graphing x+y=4 and x - y = -6?

Mar 28, 2018

The solution to the given system of equations is $\left(4 , 5\right)$.

#### Explanation:

Given:

$\text{First equation} :$$x + y = 4$

$\text{Second equation:}$ $x - y = - 6$

Find the x- and y-intercepts for each equation. Graph the points for each line separately, and draw a straight line through the points of both lines. The point at which they intersect is the solution to the system.

The x-intercept is the value of $x$ when $y = 0$.

The y-intercept is the value of $y$ when $x = 0$.

First equation

x-intercept:

Substitute $0$ for $y$.

$x + 0 = 4$

$x = 4$

The x-intercept is $\left(4 , 0\right)$.

y-intercept:

Substitute $0$ for $x$.

$0 + y = 4$

$y = 4$

The y-intercept is $\left(0 , 4\right)$.

Plot the points and draw a straight line through them.

graph{x+y=4 [-10, 10, -5, 5]}

Second equation

x-intercept:

Substitute $0$ for $y$.

x-0=-6#

$x = - 6$

The x-intercept is $\left(- 6 , 0\right)$.

y-intercept:

Substitute $0$ for $x$.

$0 - y = - 6$

$- y = - 6$

Multiply both sides by $- 1$. This will reverse the signs.

$y = 6$

The y-intercept is $\left(0 , 6\right)$.

Plot the points on the same graph and draw a straight line through them.

The point of intersection is $\left(4 , 5\right)$. This is the solution to the given system of equations.

graph{(x+y-4)(x-y+6)=0 [-10, 10, -5, 5]}