Solve x+y+z=10 −2x−2y−z=−32 3x−2y+2z=−8 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

(12, 10, -12)

x = 12

y = 10

z = -12

Step-by-step explanation:

Let's start by picking a variable to eliminate from the three equations, since "z" is at the end, let's go with "z".

Next we'll eliminate z from two of the equations by adding them together so:

(x+y+z=10) + (-2x-2y-z=-32)

you'll get: -x-y=-22

Next we'll eliminate z from the remaining equation in the same way so:

(-2x-2y-z=-32) + (3x-2y+2z=-8)

you'll get: -x-6y=-72

We now have two new equations:

-x-y=-22

-x-6y=-72

From these let's eliminate another variable, let's go with "x" and since both "x" are negative we'll multiply one of the equations by the negative sign of the other equation so we'll end up with one positive x and one negative x, which looks like this:

-x-y=-22

x+6y=72

and when we add these two equations we get:

5y=50

Finally we can solve for y:

y=10

With the known value of y we can use y to plug into the other equations and solve for the x and z variables to get x=12, y=10, z=-12