Solve the system of equations for x, y, and z. Please explain/step-by-step so I can understand. Thanks! x + y = -7
y + z = -7
x - z = 0

Step-by-step explanation:If we add the first and second equations, we will eliminate both the x and the y.

(2x + y + z) + (2x - y - z) = (3) + (9)

2x + y + z + 2x - y - z = 3 + 9

4x = 12

x = 3

So, x must equal 3.

Now, if we put 3 into each equation, we have the following equations:

6 + y + z = 3

6 - y - z = 9

3 + y - z = 0

Now, we can move all the numbers to the right side:

y + z = -3

-y - z = 3

y - z = -3

Now, we can try to eliminate another variable. If we add the second two equations, we can eliminate y.

(-y - z) + (y - z) = (3) + (-3)

-y -z + y - z = 0

-2z = 0

z = 0 (because, if we divide both sides by -2 to isolate z, 0/[-2] = 0)

So, now we have x = 3 & z = 0.

Now, pick any of the original equations and plug these values of x & z in, and you will get y.

2x + y + z = 3

2(3) + y + 0 = 3

6 + y + 0 = 3

6 + y = 3

y = -3

So, now we have x = 3, y = -3, & z = 0.

These are the only x, y, and z values that work for all 3 equations