How do you solve 2x-y=2, 3z=19, 4x+z=13

Question

You have to us the elimination method to solve the equation.

Answer 1

Substitution method

Given equations 2x-y = 2 ---> (1)

3z = 19 ---> (2)

4x+z = 13 ---> (3)

3z = 19

Divide to each side by 3.

z = 19/3

Substitute the z value in (3).

4x+19/3 = 13

Subtract 19/3 from each side.

4x = 13-19/3

4x = (39-19)/3

4x = 20/3

Divide to each side by 4.

x = 20/12

x = 5/3

Substitute x value in (1)

2(5/3)-y = 2

10/3-y = 2

Subtract 2 from each side.

-y+10/3-2 = 0

Add y to each side.

y = (10-6)/3

y = 4/3

Substitute the x value in (3).

4(5/3)+z = 13

20/3+z = 13

Subtract 20/3 from each side.

z = 13-20/3

z = (39-20)/3

z = 19/3

Solution x = 5/3, y = 4/3, z = 19/3.