y=z+7, x+z= 2 and x-y= -3

Question

How do you solve this 3 variable system problem using the substitution method?

Answer 1

Substitution method

Given equations are y = z+7 ---> (1)

x+z = 2 ---> (2)

x-y = -3 ---> (3)

From (1) substitute the y value in (3).

x-z-7 = -3

Add 7 to each side.

x-z = 4

x = z+4 ---> (4)

From (4) substitute the x value in (2).

z+4+z = 2

2z+4 = 2

Subtract 4 from each side.

2z = -2

Divide to each side by 2.

2z/2 = -2/2

⇒ z = -1

Substitute the z value in (1).

y = -1+7

⇒ y = 6

Substitute the y value in (3).

x-6 = -3

Add 6 to each side.

x-6+6 = -3+6

⇒ x = 3

Solution x = 3, y = 6, z = -1.