Solve the simultaneous linear equations for x and y: 2x + 3y = 13 and 3x - y = 3.
Answer and explanation
Correct answer: D. x = 2, y = 3
- Step 1: From the second equation: y = 3x - 3. Step 2. Substitute into first equation: 2x + 3(3x - 3) = 13 => 2x + 9x - 9 = 13 => 11x = 22 => x = 2. Step 3. Substitute back for y: y = 3(2) - 3 = 6 - 3 = 3. Answer: x = 2, y = 3. Why not the others: x = 3, y = 2 gives 2(3) + 3(2) = 12 ≠ 13; x = 4, y = 1 gives 3(4) - 1 = 11 ≠ 3; x = 1, y = 4 gives 2(1) + 3(4) = 14 ≠ 13.
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