The solution to the system of equations is x=−8 and y=0.
To solve this system of equations by substitution, we can substitute the expression for y from the second equation into the first equation:
Equation 1: 1/2 x+y=−4
Equation 2: y=2x+16
Substitute 2x+16 for y in Equation 1:
1/2 x+(2x+16)=−4
Now, combine like terms and solve for x:
1/2 x+2x+16=−4
Combine the x terms:
5/2 x+16=−4
Subtract 16 from both sides:
5/2x=−20
Multiply both sides by 2/5 to isolate x:
x=−8
Now that we have the value for x, substitute it back into one of the original equations. Let's use Equation 2:
y=2(−8)+16
y=0
So, the solution to the system of equations is x=−8 and y=0.