Solve the system: x + y = 7 and x − y = 1. What is the value of x?

Solve the system: x + y = 7 and x − y = 1. What is the value of x?

• A. 3
• B. 5
• C. 2
• D. 4

Answer: (D)

Solving a system by elimination: add the two equations so the y terms cancel, since +y and −y sum to zero. This gives (x+y) + (x−y) = 7 + 1, which simplifies to 2x = 8, so x = 4. To check, substitute into the first equation: 4 + y = 7, giving y = 3; and 4 − y = 1 also becomes 4 − 3 = 1, which confirms the solution. The value of x is 4.

Solving a system by elimination: add the two equations so the y terms cancel, since +y and −y sum to zero. This gives (x+y) + (x−y) = 7 + 1, which simplifies to 2x = 8, so x = 4. To check, substitute into the first equation: 4 + y = 7, giving y = 3; and 4 − y = 1 also becomes 4 − 3 = 1, which confirms the solution. The value of x is 4.