Final answer:
The y-value in the solution to the system of linear equations is -4.
Step-by-step explanation:
To find the y-value in the solution to this system of linear equations, we can use the method of substitution. We'll solve one of the equations for one variable and then substitute this expression into the other equation. Let's solve the second equation for y:
-2x + 3y = -16
3y = 2x - 16
y = (2/3)x - 16/3
Now, substitute this expression for y into the first equation:
4x + 5((2/3)x - 16/3) = -12
4x + (10/3)x - 80/3 = -12
Multiplying through by 3 to clear fractions:
12x + 10x - 80 = -36
22x = -36 + 80
22x = 44
x = 2
Substitute x = 2 into the expression for y:
y = (2/3)(2) - 16/3
y = 4/3 - 16/3
y = -12/3
y = -4