Solve the system using elimination: 3x + 4y = 11 and -3x + 4y = 1. Which pair (x, y) satisfies both equations?

Solve the system using elimination: 3x + 4y = 11 and -3x + 4y = 1. Which pair (x, y) satisfies both equations?

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

Answer: (A)

Elimination works well here because the x-terms have opposite coefficients, so adding the two equations cancels x and leaves an equation in y. Add the equations: (3x + 4y) + (-3x + 4y) = 11 + 1, which gives 8y = 12, so y = 12/8 = 3/2. With y found, plug into one equation to solve for x. Using 3x + 4y = 11 and y = 3/2: 3x + 4*(3/2) = 11, so 3x + 6 = 11, hence 3x = 5 and x = 5/3. Check in the other equation: -3x + 4y = 1 becomes -3*(5/3) + 4*(3/2) = -5 + 6 = 1, which matches. So the pair that satisfies both equations is x = 5/3 and y = 3/2.

Elimination works well here because the x-terms have opposite coefficients, so adding the two equations cancels x and leaves an equation in y.

Add the equations: (3x + 4y) + (-3x + 4y) = 11 + 1, which gives 8y = 12, so y = 12/8 = 3/2.

With y found, plug into one equation to solve for x. Using 3x + 4y = 11 and y = 3/2: 3x + 4*(3/2) = 11, so 3x + 6 = 11, hence 3x = 5 and x = 5/3.

Check in the other equation: -3x + 4y = 1 becomes -3*(5/3) + 4*(3/2) = -5 + 6 = 1, which matches.

So the pair that satisfies both equations is x = 5/3 and y = 3/2.