Final answer:
To find the solution of the given system of equations, we use the method of substitution. The solution is x = -3.5 and y = -4.
Step-by-step explanation:
To find the solution of the system of equations y = (3/2)x + (5/4) and -2x + 8y = -25, we can use the method of substitution. Let's solve the first equation for y:
y = (3/2)x + (5/4)
Next, substitute this value of y into the second equation:
-2x + 8((3/2)x + (5/4)) = -25
Simplify and solve for x:
-2x + 12x + 10 = -25
10x + 10 = -25
10x = -35
x = -3.5
Now, substitute the value of x back into the first equation to find y:
y = (3/2)(-3.5) + (5/4)
y = -5.25 + 1.25
y = -4
Therefore, the solution to the system of equations is x = -3.5 and y = -4.