Solve the system: 2x + 3y = 12 and 4x + y = 8.

• A. x = 3/5, y = 8/5
• B. x = 6/5, y = 16/5
• C. x = 2, y = 1
• D. x = 0, y = 4

Answer: (B)

Two linear equations in two variables intersect at a single point, which is the solution of the system. Use elimination to remove one variable and solve for the other.

Multiply the first equation by 2 to align the x terms with the second: 4x + 6y = 24. Subtract the second equation (4x + y = 8) from this: (4x + 6y) − (4x + y) = 24 − 8, giving 5y = 16, so y = 16/5.

Plug y = 16/5 into the second equation: 4x + 16/5 = 8, so 4x = 8 − 16/5 = 24/5, hence x = 6/5.

Check: 2x + 3y = 2*(6/5) + 3*(16/5) = 12/5 + 48/5 = 60/5 = 12, and 4x + y = 4*(6/5) + 16/5 = 24/5 + 16/5 = 40/5 = 8. Both hold.

The solution is x = 6/5 and y = 16/5, which matches the option with those values.