Solve the system of linear equations for x and y: 3x + 2y = 16 and 2x - y = 6. What is the value of x + y?
Answer and explanation
Correct answer: B. 6
- Step 1: Multiply the second equation by 2: 4x - 2y = 12.
- Step 2: Add to the first equation: (3x + 2y) + (4x - 2y) = 16 + 12 => 7x = 28 => x = 4.
- Step 3: Substitute x = 4 into 2x - y = 6: 2(4) - y = 6 => 8 - y = 6 => y = 2.
- Step 4: Calculate the requested sum: x + y = 4 + 2 = 6.
Answer
6.
Why not the others: Option 4 represents only the value of x. Option 2 represents only the value of y. Option 8 adds 2x to y incorrectly.
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