If 12x - 7y = 9 and 4x + 7y = 39, what is the value of 2x - y?
Answer and explanation
Correct answer: 15/7
Add the equations to eliminate y: (12x - 7y) + (4x + 7y) = 9 + 39. This gives 16x = 48, so x = 3. Substitute x = 3 into 4x + 7y = 39: 12 + 7y = 39, hence 7y = 27 and y = 27/7. Therefore 2x - y = 2(3) - 27/7 = 6 - 27/7 = 42/7 - 27/7 = 15/7. Option B is correct. The values 2, 4, and 5 are distractors that may arise from using only one equation or from neglecting the fractional value of y; direct substitution verifies that 15/7 is exact.
Frequently asked questions
What is the correct answer to this question?
15/7
Why is this the correct answer?
Add the equations to eliminate y: (12x - 7y) + (4x + 7y) = 9 + 39. This gives 16x = 48, so x = 3. Substitute x = 3 into 4x + 7y = 39: 12 + 7y = 39, hence 7y = 27 and y = 27/7. Therefore 2x - y = 2(3) - 27/7 = 6 - 27/7 = 42/7 - 27/7 = 15/7. Option B is correct. The values 2, 4, and 5 are distractors that may arise from using only one equation or from neglecting the fractional value of y; direct substitution verifies that 15/7 is exact.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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