Solve by elimination Indicate if the system is inconsistent

Solve by elimination. Indicate if the system is inconsistent or has an infinite number of solutions. Leave your final answers in fractional form, do NOT use decimals. Show work plz

2x + 5y + 3z = 3,

4x + 2y + 2z = 1,

2x 3y + 2z = 5

Solution

2x + 5y + 3z = 3,

4x + 2y + 2z = 1,

2x 3y + 2z = 5

Elimination method:

Multiply first equation by 2 and add the result to the second equation. The result is:

2x + 5y + 3z = 3,

-8y -4z = -5,

2x 3y + 2z = 5

Multiply first equation by 1 and add the result to the third equation. The result is:

2x + 5y + 3z = 3,

-8y -4z = -5,

-8y -z = 2

Multiply second equation by 1 and add the result to the third equation. The result is

3z =7

z= 7/3

solve for y.: -8y -4z = -5,

y = -13/24

solve for x by substituting y=13/24 and z=7/3 into the first equation.

x = 31/48