How to solve this problem - Algebra

Question

x + y + z = 30

x - y - z = 96

x - y + z = -96

x =

y =

z =

Answer 1

Add the first two equations to get 2x = 126. So, x = 63.

Subtract the third equation from the first to get 2y = 126. So, y = 63.

Substituting into the equation x - y + z = -96, we have z = -96.

Solution: x = y = 63, and z = -96

Answer 2

This is pretty easy if you use the method called Elimination to solve.

First add the Equation #1 and Equation #2 together:

x + y + z = 30

x - y - z = 96

-----------------

2x = 126

x = 63

Then multiply Equation #3 by -1 and add the results to Equation 2

x - y - z = 96

-x + y - z = 96

------------------

-2z = 192

z = -96

Then plug in the two answers (x = 63 and z = -96) into Equation #1 and solve for y

63 + y - 96 = 30

y - 33 = 30

y = 63

So:

x = 63

y = 63

z = -96