Question

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

Answer 1

The solution to the given system of equations is `(4,5)`.

Explanation:

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]}