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

Question

{2x+y=9}

{x-2z=-3}

{2y+3z=15}

Answer 1

Substitution method

Given first equation 2x + y  = 9

Subtract 2x  from each side.

y = -2x + 9 ---> (1)

Second equation x - 2z = -3  ---> (2)

Third equation 2y + 3z = 15

From (1) substitute y  value in above equation.

2(-2x + 9) + 3z = 15

-4x + 18 + 3z = 15

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

Multiple to each side  of equation (2) by 4.

4x - 8z = -12 ---> (4)

To eliminate the  x  value add the equations (3)&(4).

-4x + 3z = -3

4x - 8z = -12

_________________

-5z = -15

Divide each side by negitive 5.

z = 3.

Substitute z  value in (2).

x - 6 = -3

Add 6 to each side.

x = 3

Substitute x value in 2x + y = 9.

6 + y = 9

Subtract 6 from each side.

y  = 3.

Solution x  = 3, y  = 3, z  = 3.