Solve the linear system: x + y = 7 and 2x - y = 1. What are x and y?

Solve the linear system: x + y = 7 and 2x - y = 1. What are x and y?

• A. x = 3, y = 4
• B. x = 7/2, y = 0.5
• C. x = 8/3, y = 13/3
• D. x = 2, y = 5

Answer: (C)

Solving a linear system by substitution: take one equation to express one variable in terms of the other, then substitute into the second equation. From the first equation, y = 7 − x. Substitute this into the second equation: 2x − (7 − x) = 1, which simplifies to 3x − 7 = 1, so x = 8/3. Then y = 7 − 8/3 = 13/3. Check: x + y = 8/3 + 13/3 = 7 and 2x − y = 16/3 − 13/3 = 1, so the solution is x = 8/3 and y = 13/3.

Solving a linear system by substitution: take one equation to express one variable in terms of the other, then substitute into the second equation. From the first equation, y = 7 − x. Substitute this into the second equation: 2x − (7 − x) = 1, which simplifies to 3x − 7 = 1, so x = 8/3. Then y = 7 − 8/3 = 13/3. Check: x + y = 8/3 + 13/3 = 7 and 2x − y = 16/3 − 13/3 = 1, so the solution is x = 8/3 and y = 13/3.