Solve the following system of equations What is the value of y when x - y - z equals 0 3x plus y - z equals 2 x plus 2y plus z equals 0?

Answer 1

x = -1, y = 2, z = -3.

1. x - y - z = 0
2. 3x + y - z = 2
3. x + 2y + z = 0

Adding equation 3 to equations 1 and 2 gives new equations 1 & 2:

1. 2x + y = 0
2. 4x + 3y = 2

Doubling the [new] equation 1 and subtracting from the [new] equation 2 gives:

• y = 2

Substituting back into [new] equation 1 gives:

• 2x + 2 = 0 ==> x = -1

Substituting back into the original equation 1 gives:

• -1 - 2 - z = 0 ==> z = -3

Check by substituting back into original equations:

• 3x + y - z = 3(-1) + (2) - (-3) = -3 + 2 + 3 = 2
• x + 2y + z = (-1) + 2(2) + (-3) = -1 + 4 - 3 = 0