Final answer:
To solve the given system of equations using the elimination method, we need to multiply the equations by appropriate amounts to eliminate the y variable. By multiplying the first equation by 3 and the second equation by 2, we can add the equations together to eliminate y. After solving for x, we substitute the value of x back into one of the original equations to solve for y. The solution to the system of equations is (x, y) = (12, -1).
Step-by-step explanation:
To solve the system of equations using the elimination method, we will multiply the first equation by 3 and the second equation by 2. This will allow us to eliminate the y variable.
Multiplying the first equation by 3, we get 3x - 6y = 42.
Multiplying the second equation by 2, we get 2x + 6y = 18.
Adding these two equations together, we get 5x = 60.
Dividing both sides by 5, we find that x = 12.
Substituting x = 12 back into the first equation, we can solve for y. 12 - 2y = 14. Rearranging the equation, we get -2y = 2. Dividing both sides by -2, we find that y = -1.
Therefore, the solution to the system of equations is (x, y) = (12, -1).