Final answer:
To solve the system of equations using the elimination method, we multiply the first equation by 2 and subtract the second equation from it to eliminate the x variable. The solution to the system of equations is x = 2 and y = -1.
Step-by-step explanation:
To use the elimination method to find all solutions of the system of equations, we eliminate one variable by multiplying one or both of the equations by a constant so that the coefficients of one variable become equal and opposite. In this case, we can multiply the first equation by 2 to get 8x - 6y = 22. Then, we can subtract the second equation from the modified first equation to eliminate the x variable. This gives us (8x - 6y) - (8x + 4y) = 22 - 12, which simplifies to -10y = 10. Solving for y, we get y = -1. Substituting the value of y into the first equation, we get 4x - 3(-1) = 11, which simplifies to 4x + 3 = 11. Solving for x, we get x = 2.