Final answer:
To solve the system of equations, we add the equations together to eliminate 'x' and solve for 'y', then substitute the value of 'x' back into one of the equations to solve for 'y'. The solution to the system of equations is (x, y) = (3, -1).
Step-by-step explanation:
To solve the system of equations using the linear combination method, we need to eliminate one variable. In this case, we can eliminate the variable 'x' by adding the two equations together. Adding the equations gives us: (x + 2y) + (x - 2y) = 1 + 5, which simplifies to 2x = 6. Dividing both sides by 2, we find that x = 3.
Substituting the value of x back into either of the original equations, we can solve for y. Plugging x = 3 into the first equation, we have: 3 + 2y = 1. Subtracting 3 from both sides, 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) = (3, -1).