Answer: No Solution
I am going to take a guess that we are solving the problem.
First, let's multiply the first equation by 3 and the second equation by 2 to eliminate the z term:
-15y + 6z = -60 (Equation 1)
8x + 6z = 10 (Equation 2)
(-15y + 6z) - (8x + 6z) = -60 - 10
-15y + 6z - 8x - 6z = -70
-15y - 8x = -70
-120y - 64x = -560
-(-15y - 8x) = -(-70)
-120y - 64x = -560
15y + 8x = 70
(-120y - 64x) + (15y + 8x) = -560 + 70
-105y - 56x = -490
Now we have two equations:
-15y - 8x = 70
-105y - 56x = -490
-105y - 56x - (-105y - 56x) = -490 - (70 * 7)
0 = -980
The system of equations -5y + 2z = -20 and 4x + 3z = 5 has no solution.