Solve the system by substitution.⎧⎩⎨⎪⎪−x−y−z=−8−4x+4y+5z=72x+2z=4

Answer 1

From the third equation, we can isolate x to get x = 4 - 2z.
Then we substitute this expression for x in the first equation:
-(4 - 2z) - y - z = -8
Simplifying this equation, we get -4 + 2z - y - z = -8
Combining like terms, we have -4 - y - 2z = -8
Rearranging this equation, we get y + 2z = 4.

Now we substitute x = 4 - 2z from the third equation into the second equation:
-4(4 -2z) + 4y + 5z = 72
Simplifying this equation, we get -16 + 8z + 4y + 5z = 72
Combining like terms, we have 13z + 4y = 88.

So we have the system of equations:
y + 2z = 4
13z + 4y = 88

To solve the system by substitution, we can isolate y:
y = 4 - 2z

Now substitute this expression for y in the second equation:
13z + 4(4 - 2z) = 88
Simplifying this equation, we get 13z + 16 - 8z = 88
Combining like terms, we have 5z + 16 = 88
Subtracting 16 from both sides, we get 5z = 72
Dividing by 5, we find z = 14.4.

Now substitute this value for z in y = 4 - 2z:
y = 4 - 2(14.4) = 4 - 28.8 = -24.8.

Finally, substitute z = 14.4 into x = 4 - 2z:
x = 4 - 2(14.4) = 4 - 28.8 = -24.8.

Therefore, the solution to the system is x = -24.8, y = -24.8, and z = 14.4.