Solve the following systems of equations:x - y + z = 4x + y + z = 22x

1.	Solve the following systems of equations:x - y + z = 4x + y + z = 22x + y - 3z = 0
Answer» 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

Solve the following systems of equations:x - y + z = 4x + y + z = 22x + y - 3z = 0

Answer»

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