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

Given:

#"First equation":##x+y=4#

#"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 #(4,0)#.

y-intercept:

Substitute #0# for #x#.

#0+y=4#

#y=4#

The y-intercept is #(0,4)#.

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 #(-6,0)#.

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 #(0,6)#.

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

The point of intersection is #(4,5)#. This is the solution to the given system of equations.

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