The calculated solutions to the systems of equations are (2, 16), (11, -7) and (3, 4)
How to determine the solution to the systems
From the question, we have the following parameters that can be used in our computation:
y = 9x - 2
y = 3x + 10
By substitution, we have
9x - 2 = 3x + 10
So, we have
6x = 12
x = 2
Recall that
y = 9x - 2
y = 9 * 2 - 2
y = 16
Hence, the solution is (2, 16)
Next, we have
y = -x + 4
5x + 6y = 13
By substitution, we have
5x + 6(-x + 4) = 13
5x - 6x + 24 = 13
This gives
x = 11
Recall that
y = -x + 4
y = -11 + 4
y = -7
Hence, the solution is (11, -7)
Next, we have
-3x + 4y = 7
y = 3x - 5
By substitution, we have
-3x + 4(3x - 5) = 7
-3x + 12x - 20 = 7
9x = 27
This gives
x = 3
Recall that
y = 3x - 5
y = 3 * 3 - 5
y = 4
Hence, the solution is (3, 4)