Solve the system of equations for x and y: 3x + 2y = 16 and 2x - y = 6.
Answer and explanation
Correct answer: C. x = 4 and y = 2
- Step 1: From the second equation, express y: y = 2x - 6.
- Step 2: Substitute into first equation: 3x + 2(2x - 6) = 16.
- Step 3: Simplify: 3x + 4x - 12 = 16, so 7x = 28, giving x = 4.
- Step 4: Find y: y = 2(4) - 6 = 8 - 6 = 2.
Answer
x = 4 and y = 2.
Why not the others: 'x = 2 and y = 4' swaps the variable coordinates; 'x = 6 and y = -1' satisfies neither equation; 'x = 3 and y = 3' yields 3(3) + 2(3) = 15 != 16.
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