Solve the system: x + y = 7 and x - y = 1. Find x and y.

Solve the system: x + y = 7 and x - y = 1. Find x and y.

• A. x=3, y=4
• B. x=4, y=3
• C. x=5, y=2
• D. x=2, y=5

Answer: (B)

When solving a two-equation, two-variable system, you can use elimination by adding the equations to remove one variable. Add the two given equations: (x + y) + (x − y) = 7 + 1. The y terms cancel, leaving 2x = 8, so x = 4. Now substitute x = 4 into the first equation: 4 + y = 7, which gives y = 3. The pair x = 4 and y = 3 makes both equations true, since 4 + 3 = 7 and 4 − 3 = 1. Any other listed pair won’t satisfy both equations simultaneously.

When solving a two-equation, two-variable system, you can use elimination by adding the equations to remove one variable. Add the two given equations: (x + y) + (x − y) = 7 + 1. The y terms cancel, leaving 2x = 8, so x = 4. Now substitute x = 4 into the first equation: 4 + y = 7, which gives y = 3. The pair x = 4 and y = 3 makes both equations true, since 4 + 3 = 7 and 4 − 3 = 1. Any other listed pair won’t satisfy both equations simultaneously.