Final answer:
To solve the system of equations by the elimination method, you want to eliminate one variable by adding or subtracting the equations together. In this case, we can eliminate the x variable by multiplying the first equation by 2 and the second equation by 3, making the x terms cancel out.
Step-by-step explanation:
To solve the system of equations by the elimination method, you want to eliminate one variable by adding or subtracting the equations together. In this case, we can eliminate the x variable by multiplying the first equation by 2 and the second equation by 3, making the x terms cancel out.
After multiplying the first equation by 2, we have 8y + 6x = 36. After multiplying the second equation by 3, we have -24y + 9x = -54. Now we can subtract the second equation from the first equation to eliminate x: (8y + 6x) - (-24y + 9x) = 36 - (-54)
Simplifying: 32y + 3x = 90. Now we have a new system of equations: 32y + 3x = 90 and -24y + 9x = -54. From here, you can solve for one variable and substitute that value back into one of the original equations to solve for the other variable.