The correct solution to the system of equations y=2x and y=-x+6 is A) x = 2, y = 4, determined by setting the equations equal to each other and solving for x, and then substituting that value for x back into one of the original equations to find y.
The solution to the system of equations y=2x and y=-x+6 is determined by finding the intersection point of the two lines represented by these equations. To find the solution, one can set the two equations equal to each other because they both equal y. This results in 2x = -x + 6. Solving this equation, we add x to both sides to get 3x = 6, then divide by 3 to get x = 2. Substituting x back into one of the original equations, y = 2(2), we find that y = 4. Thus the correct solution where the two lines intersect is A) x = 2, y = 4.
Answer is: The correct solution to the system of equations is A) x = 2, y = 4.
In conclusion, by equalizing the two given linear equations and solving for x, then substituting x back into one of the equations to find y, we confirm that the solution is indeed x = 2 and y = 4, which is option A.