If 3(x + y) + 4(x - y) = 59 and 5(x + y) - 2(x - y) = 37, what is the value of x?
Answer and explanation
Correct answer: 225/26
Use a change of variables to simplify the repeated expressions. Let u = x + y and v = x - y. The equations become 3u + 4v = 59 and 5u - 2v = 37. Multiply the second equation by 2, obtaining 10u - 4v = 74. Adding it to the first gives 13u = 133, so u = 133/13. Substituting into 3u + 4v = 59 gives v = 92/13. Since u + v = 2x, x = (133/13 + 92/13)/2 = 225/26. Hence option B is correct. The integer distractors do not satisfy the transformed equations.
Frequently asked questions
What is the correct answer to this question?
225/26
Why is this the correct answer?
Use a change of variables to simplify the repeated expressions. Let u = x + y and v = x - y. The equations become 3u + 4v = 59 and 5u - 2v = 37. Multiply the second equation by 2, obtaining 10u - 4v = 74. Adding it to the first gives 13u = 133, so u = 133/13. Substituting into 3u + 4v = 59 gives v = 92/13. Since u + v = 2x, x = (133/13 + 92/13)/2 = 225/26. Hence option B is correct. The integer distractors do not satisfy the transformed equations.
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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