How do you solve for equations x-y-z equals 1 2x plus y-z equals 1 x-y plus 2z equals 7?

Answer 1

(1) x - y - z = 1

(2) 2x + y - z = 1

(3) x - y + 2z = 7

With linear equations involving three unknowns use different pairs of equations to eliminate the same unknown. This will result in two (or perhaps three if needed) equations containing two unknowns.

For this exercise, eliminate z as the first step.

Subtract equation (1) from equation (2)

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

Multiply equation (2) by 2 then add to equation (3)

4x + 2y - 2z + x - y + 2z = 2 + 7 : (5) 5x + y = 9

Multiply equation (5) by 2 then subtract equation (4)

10x + 2y - (x + 2y) = 18 - 0 : 9x = 18 : x = 2

Substituting for x in equation (5) gives 10 + y = 9 : y = -1

Substituting for x and y in equation (2) gives 4 -1 -z = 1 : z = 2