Final answer:
The system of equations x + y = 2 and 4x - 2y = 8 is solved by elimination, resulting in the solution (2, 0) after multiplying the first equation by 2 and adding them together to eliminate y.
Step-by-step explanation:
To solve the system of equations x + y = 2 and 4x - 2y = 8 by elimination, we must first make the coefficients of either x or y the same in both equations to eliminate one of the variables when we add or subtract the equations from each other.
Let's multiply the first equation by 2, giving us 2x + 2y = 4. Now, we have the system:
Adding these two equations, we get 6x = 12, which simplifies to x = 2 when divided by 6. Substituting x = 2 back into the first original equation x + y = 2, we get 2 + y = 2, which simplifies to y = 0. Therefore, the solution to the system of equations is (2, 0).