If 4(2x - y) + 3(x + y) = 53 and 2(2x - y) - 5(x + y) = -17, what is the value of y?
Answer and explanation
Correct answer: 67/39
Let u = 2x - y and v = x + y. The equations then become 4u + 3v = 53 and 2u - 5v = -17. Multiply the first equation by 5 and the second by 3: 20u + 15v = 265 and 6u - 15v = -51. Adding gives 26u = 214, so u = 107/13. Using 2u - 5v = -17 gives v = 87/13. To recover y, note that 2v - u = 2(x + y) - (2x - y) = 3y. Therefore y = (2v - u)/3 = (174/13 - 107/13)/3 = 67/39. Option B is correct; the integer choices do not satisfy the original pair.
Frequently asked questions
What is the correct answer to this question?
67/39
Why is this the correct answer?
Let u = 2x - y and v = x + y. The equations then become 4u + 3v = 53 and 2u - 5v = -17. Multiply the first equation by 5 and the second by 3: 20u + 15v = 265 and 6u - 15v = -51. Adding gives 26u = 214, so u = 107/13. Using 2u - 5v = -17 gives v = 87/13. To recover y, note that 2v - u = 2(x + y) - (2x - y) = 3y. Therefore y = (2v - u)/3 = (174/13 - 107/13)/3 = 67/39. Option B is correct; the integer choices do not satisfy the original pair.
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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