Final answer:
To solve the system of equations, substitute the value of y from the second equation into the first equation. Then solve for x and substitute the value of x back into the second equation to find y. The solution is x = -12 and y = 3.
Step-by-step explanation:
To solve the system of equations 1/2x + 6y = 12 and y = x + 15, we can use substitution method. We'll substitute the value of y from the second equation into the first equation.
Substituting y = x + 15 into the first equation, we get 1/2x + 6(x + 15) = 12. Now we can solve for x.
Expanding the equation, we get 1/2x + 6x + 90 = 12. Combining like terms, we have 6.5x = -78. Dividing both sides by 6.5, we find x = -12.
Now we can substitute the value of x back into the second equation to find y. Substituting x = -12 into y = x + 15, we have y = -12 + 15. Simplifying, we get y = 3.
So the solution to the system of equations is x = -12 and y = 3.