Solve the system: 3x + y = 9 and y = -x + 3.

• A. (2, 3)
• B. (0, 9)
• C. (3, 0)
• D. (1, 6)

Answer: (C)

When solving a system of linear equations, you look for the point where the two lines intersect. Use substitution by replacing y in the first equation with the expression for y from the second equation.

From the second equation, y = -x + 3. Substitute into 3x + y = 9 to get 3x + (-x + 3) = 9, which simplifies to 2x + 3 = 9. So 2x = 6, and x = 3. Then y = -3 + 3 = 0. The solution is the point (3, 0), which satisfies both equations, so it’s the intersection of the two lines. The other candidate points don’t satisfy the second equation (or both equations) and thus aren’t solutions.