y=z+7 x+z= 2 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

Add z to each side.

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

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

z+4+z = 2

2z+4 = 2

Add 10 to each side.

2z = -2

Divide to each side by 2.

z = -1

Substitute z value in (1).

y = 6

Substitute y value in (3).

x-6 = -3

x = 3

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