solve 2x+y=9, x-2z=-3, and 2y+3z=15

Question

{2x+y=9}

{x-2z=-3}

{2y+3z=15}

Answer 1

solve 2x+y=9, x-2z=-3, and 2y+3z=15

Equation 2:
x - 2z = -3
x = 2z - 3   use that in equation 1

Equation 1:
2x + y = 9
2(2z - 3) + y = 9
4z - 6 + y = 9
4z + y = 15
Multiply by 2 so we can use it with equation 3.
2 * (4z + y) = 15 * 2
8z + 2y = 30
2y + 8z = 30       same order as equation 3

  2y + 8z = 30
-(2y + 3z = 15)
---------------------
          5z = 15
z = 3     <<<<<<<<<<<<<<<<<<<<

Use that in equation 2.
x - 2z = -3
x - 2(3) = -3
x - 6 = -3
x = 3     <<<<<<<<<<<<<<<<<<<<

Use that value in equation 1.
2x + y = 9
2(3) + y = 9
6 + y = 9
y = 3     <<<<<<<<<<<<<<<<<<<<

All three variables equal 3.