Solving 5x−12y=−1 and 10x+12y=61, what is the value of xy?
Answer and explanation
Correct answer: 7
Use elimination first, then calculate the requested product. Adding the equations removes y because the coefficients are −12 and +12: 15x = −1 + 61 = 60. Hence x = 4. Substitute this into 5x − 12y = −1: 20 − 12y = −1, so −12y = −21 and y = 21/12 = 7/4. Therefore xy = 4 × 7/4 = 7. Option A is correct. A quick check in the second equation gives 10(4) + 12(7/4) = 40 + 21 = 61. The originally supplied options and marked answer did not contain 7, so the options have been corrected; calculating only x or y would not answer the question.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Use elimination first, then calculate the requested product. Adding the equations removes y because the coefficients are −12 and +12: 15x = −1 + 61 = 60. Hence x = 4. Substitute this into 5x − 12y = −1: 20 − 12y = −1, so −12y = −21 and y = 21/12 = 7/4. Therefore xy = 4 × 7/4 = 7. Option A is correct. A quick check in the second equation gives 10(4) + 12(7/4) = 40 + 21 = 61. The originally supplied options and marked answer did not contain 7, so the options have been corrected; calculating only x or y would not answer the question.
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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