Final answer:
To solve the system, substitute y from the first equation into the second, simplify and solve for x, then substitute x back into the first equation to find y. The solution is x = -2, y = 0.
Step-by-step explanation:
To solve the given system of equations algebraically, we need to either use the substitution method or the elimination method. Since the first equation is already solved for y, it makes sense to use the substitution method.
The system is:
y = (3/2)x + 3
5x + 5y = -10
Substitute the expression for y from the first equation into the second equation:
5x + 5((3/2)x + 3) = -10
Distribute the 5:
5x + (15/2)x + 15 = -10
Combine like terms (multiply the fractions by 2 for easier addition):
(10/2)x + (15/2)x = -25
(25/2)x = -25
Divide both sides by (25/2):
x = -25 / (25/2)
x = -25 * (2/25)
x = -2
Now solve for y by substituting x back into the first equation:
y = (3/2)(-2) + 3
y = -3 + 3
y = 0
The solution to the system of equations is x = -2, y = 0.