Question

Explain, in complete sentences, how you would use the graphing method to solve the following system of equations. Provide the solution to the system and explain what the solution represents on the graph.

x + 4y = -16
3x + 2y = 12

Answer 1

@texaschic101

Answer 2

x + 4y = -16
4y = -x - 16
y = -1/4x - 4
In y = mx + b form, the m is the slope and the y intercept is b.
So the slope is -1/4, and the y intercept is (0,-4)

To find the x intercept, sub in 0 for y and solve for x
x + 4(0) = -16
x = -16 .....x intercept is (-16,0)

Plot your intercepts...(0,-4) and (-16,0)

start at the x intercept (-16,0) and since the slope is -1/4, you come down 1(because it is negative), then go to the right 4, then down 1, and to the right 4, and you will eventually cross the y axis at (0,-4)

3x + 2y = 12
2y = -3x + 12
y = -3/2x + 6

slope = -3/2 and y intercept = (0,6)
x intercept = 3x + 2(0) = 12, 3x = 12, x = 4 ...x int = (4,0)

plot your intercepts...(0,6) and (4,0)

start at y int (0,6) and since slope is -3/2, go down 3, and to the right 2, then down 3, and to the right 2, and you will eventually cross the x axis at (4,0)

Once your lines are graphed, you will find that they intersect at (8,-6) -- your solution

It can be checked algebraically...
x + 4y = -16 --->(-3)
3x + 2y = 12
------------
-3x - 12y = 48 (result of multiplying by -3)
3x + 2y = 12
------------add
-10y = 60
y = -6
now sub -6 in for y
x + 4y = -16
x + 4(-6) = -16
x - 24 = -16
x = 24 - 16
x = 8
so your solution is (8,-6)

Your final solution is (8,-6) and it checks out algebraically as well.

I am sorry that I am writing so much...I just want you to understand