Solve the system: 2x + y = 7 and 4x - y = 5.

Solve the system: 2x + y = 7 and 4x - y = 5.

• A. x=1, y=4
• B. x=3, y=2
• C. x=2, y=3
• D. x=0, y=7

Answer: (C)

Solving this system uses the elimination idea: combine the equations in a way that one variable drops out so you can solve for the other. The two equations are 2x + y = 7 and 4x − y = 5. The y terms have opposite signs, so adding the equations makes y cancel: (2x + y) + (4x − y) = 7 + 5, giving 6x = 12, which yields x = 2. Now plug x = 2 back into one equation to find y. Using 2x + y = 7 gives 2(2) + y = 7, so 4 + y = 7, and y = 3. The intersection point of the two lines is x = 2 and y = 3, which satisfies both equations (and you can check: 4x − y = 8 − 3 = 5).

Solving this system uses the elimination idea: combine the equations in a way that one variable drops out so you can solve for the other. The two equations are 2x + y = 7 and 4x − y = 5. The y terms have opposite signs, so adding the equations makes y cancel: (2x + y) + (4x − y) = 7 + 5, giving 6x = 12, which yields x = 2. Now plug x = 2 back into one equation to find y. Using 2x + y = 7 gives 2(2) + y = 7, so 4 + y = 7, and y = 3. The intersection point of the two lines is x = 2 and y = 3, which satisfies both equations (and you can check: 4x − y = 8 − 3 = 5).