Question

Solve the following systems of equations:

x - y + z = 4

x + y + z = 2

2x + y - 3z = 0

Answer 1

x - y + z = 4

x + y + z = 2

2x + y - 3z = 0

Adding eq 1 and eq2

⇒ 2(x + z) = 6

⇒ x = 3 – z

(3) – (2) – (1)

⇒ y – 5z = - 4

⇒ y = - 4 + 5z

Substituting in eq2

⇒ 3 – z - 4 + 5z + z = 2

⇒ 5z = 3

⇒ z = 3/5

Thus,

x = 3 – z

⇒ x = 12/5 Y = 5z – 4

⇒ y = -1