Solve the system of equations: 2x + y = 5 and x - y = 1.

• A. x = 2, y = 1
• B. x = 1, y = 2
• C. x = 3, y = -1
• D. x = 0, y = 5

Answer: (A)

Using elimination to solve a pair of linear equations is natural when the equations share a variable with opposite signs. Here the y terms have coefficients +1 and -1, so adding the two equations cancels y. Adding 2x + y = 5 and x − y = 1 gives 3x = 6, so x = 2. Substituting x = 2 into x − y = 1 yields 2 − y = 1, which gives y = 1. So the solution is x = 2 and y = 1, which satisfies both equations. The other listed pairs don’t satisfy at least one of the equations.