Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this 4x - y = -5
x + 2y = -8
I need to graph the lines and I have completely forgotten how to solve. Just need a refresher. Thanks!

Plot the following points on the graph:

4x - y = -5:  (0, 5), (-5/4, 0)

x + 2y = -8: (0, -4), (-8, 0)

Step-by-step explanation:

4x - y = -5

x + 2y = -8

Solving system graphically involves finding at least 2 pairs of points for each linear equation to plot. Since you have 2 linear equations, then it means that you need at least 4 pairs of coordinates to plot on your graph. The x- and y-intercepts are often used for solving systems of linear equations graphically.  

Start by transforming both equations into its slope-intercept form: y = mx + b

4x - y = -5

Subtract 4x from both sides:

4x - 4x - y = - 4x - 5

-y = -4x - 5

Divide both sides by -1, which results into:

y = 4x + 5 (this is your linear equation for 4x - y = -5).

By definition, the y-intercept is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.  The y-coordinate of your y-intercept is 5, which means its coordinates is (0, 5).

The x-intercept is the point on the graph where it crosses the x-axis. It is also the value of x when y = 0.

You could find the x-intercept by setting y = 0:

y = 4x + 5

0 = 4x + 5

Subtract 5 from both sides:

0 - 5 = 4x + 5 - 5

-5 = 4x

Divide both sides by 4:

-5/4 = x

Therefore, the x-intercept = (-5/4, 0).

x + 2y = -8

Do the same process for this equation.

Subtract x from both sides:

x - x + 2y = - x - 8

2y = -x - 8

Divide both sides by 2:

y = - ½x - 4

The y-coordinate of your y-intercept is -4,  which means that the y-intercept = (0, -4).  

Solve for the x-intercept by setting y = 0:

y = - ½x - 4

0 = - ½x - 4

Add 4 to both sides:

0 + 4 = - ½x - 4 + 4

4 = - ½x

Multiply both sides by -2:

(-2) 4 = (-2) -½x

-8 = x

Therefore, the x-intercept = (-8, 0).

4x - y = -5:  (0, 5), (-5/4, 0)

x + 2y = -8: (0, -4), (-8, 0)

Now that you have 2 pairs of coordinates for each linear equation, you can plot these points on the graph. The intersection of these lines will be your solution.

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