Final answer:
To solve the system of equations, use the method of elimination or substitution. Multiply the first equation by 2 to make the coefficients of y equal in both equations. Add the two equations and simplify. Solve for y, then substitute the value of y into either of the original equations to solve for x. The solution is (4, 3).
Step-by-step explanation:
To solve the system of equations 2x + 2y = 14 and 4x - 2y = 10, we can use the method of elimination or substitution. Here, let's use the method of elimination:
- Multiply the first equation by 2 to make the coefficients of y in both equations equal. This gives us: 4x + 4y = 28
- Add this equation to the second equation: (4x + 4y) + (4x - 2y) = 28 + 10
- Simplify by combining like terms: 8x + 2y = 38
- Divide the entire equation by 2 to solve for y: 4x + y = 19
- Substitute this value of y in either of the original equations to solve for x. Using the first equation, we have: 2x + 2(19 - 4x) = 14
- Simplify and solve for x: 2x + 38 - 8x = 14. This gives us -6x = -24, and x = 4.
- Now substitute this value of x in either of the original equations to solve for y. Using the first equation: 2(4) + 2y = 14
- Simplify and solve for y: 8 + 2y = 14. This gives us 2y = 6, and y = 3.
Therefore, the solution to the system of equations is (4, 3), which corresponds to option A.