Solve for x and y: 5x − 2y = 1 and x + y = 10.

• A. x = 4, y = 6
• B. x = 3, y = 7
• C. x = 5, y = 5
• D. x = 14, y = -4

Answer: (B)

Solving a pair of linear equations often uses substitution. Use one equation to express one variable in terms of the other, then plug that into the other equation. From x plus y equals 10, express y as 10 minus x. Substitute into 5x minus 2y equals 1: 5x minus 2(10 minus x) equals 1, which simplifies to 7x minus 20 equals 1, so 7x equals 21 and x equals 3. Then y equals 10 minus x, giving y equals 7. Checking both equations confirms the solution: 5(3) minus 2(7) equals 1, and 3 plus 7 equals 10. Other listed pairs don’t satisfy the first equation when substituted, so they’re not solutions.