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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!

Sagot :

djtwinx017

Answer:

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.

Please mark my answers as the Brainliest if you find my explanations helpful :)

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