Final answer:
To solve the system of equations x + 2y = 6 and 2x + y = 6, you can use the method of elimination. The solution to the system of equations is (x, y) = (2, 2), which corresponds to answer choice b) (0, 6).
Step-by-step explanation:
To solve the system of equations, x + 2y = 6 and 2x + y = 6, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the second equation by 2, which gives us 4x + 2y = 12. Now we can subtract the first equation from the second equation to eliminate the x variable: (4x + 2y) - (x + 2y) = 12 - 6. Simplify the equation to get 3x = 6, and solve for x by dividing both sides by 3: x = 2.
Substitute the value of x back into one of the original equations to solve for y. Using the first equation, we have 2 + 2y = 6. Subtract 2 from both sides to isolate the y variable: 2y = 4. Lastly, solve for y by dividing both sides by 2: y = 2.
Therefore, the solution to the system of equations is (x, y) = (2, 2), which corresponds to answer choice b) (0, 6).