The solution to the system of equations is x = 2 and y = -8. This was found by eliminating variables through subtraction, leading to a consistent and unique solution for both unknowns.
To solve the system of equations using elimination, we can manipulate one or both equations to eliminate one of the variables when the equations are added or subtracted. Let's work through the given system:
Equation 1: 6x + 3y = -12
Equation 2: 6x + 2y = -4
To eliminate one of the variables, we can subtract Equation 2 from Equation 1:
(6x + 3y) - (6x + 2y) = -12 - (-4)
Simplifying both sides:
6x + 3y - 6x - 2y = -12 + 4
Combining like terms:
y = -8
Now that we have the value for y, we can substitute it back into one of the original equations to find x. Let's use Equation 1:
6x + 3(-8) = -12
Simplify and solve for x:
6x - 24 = -12
6x = 12
x = 2
So, the solution to the system of equations is x = 2 and y = -8.
Complete question:
Solve the system using elimination.
6x + 3y = –12
6x + 2y = –4