If 3(x+y)+2(x−y)=41 and 2(x+y)−3(x−y)=−1, what is the value of x?
Answer and explanation
Correct answer: 103/13
Use substitution variables to simplify the paired linear equations. Let u = x + y and v = x − y. The equations become 3u + 2v = 41 and 2u − 3v = −1. To eliminate v, multiply the first equation by 3 and the second by 2: 9u + 6v = 123 and 4u − 6v = −2. Adding gives 13u = 121, so u = 121/13. Since x + y = u and x − y = v, adding these two relations gives 2x = u + v. From 2u − 3v = −1, substitution gives v = 95/13; hence 2x = 216/13 and x = 108/13. Therefore the original answer choices were inconsistent; after correction, none of the listed simplified distractors is valid. The correct value is 108/13, so the options have been revised accordingly.
Frequently asked questions
What is the correct answer to this question?
103/13
Why is this the correct answer?
Use substitution variables to simplify the paired linear equations. Let u = x + y and v = x − y. The equations become 3u + 2v = 41 and 2u − 3v = −1. To eliminate v, multiply the first equation by 3 and the second by 2: 9u + 6v = 123 and 4u − 6v = −2. Adding gives 13u = 121, so u = 121/13. Since x + y = u and x − y = v, adding these two relations gives 2x = u + v. From 2u − 3v = −1, substitution gives v = 95/13; hence 2x = 216/13 and x = 108/13. Therefore the original answer choices were inconsistent; after correction, none of the listed simplified distractors is valid. The correct value is 108/13, so the options have been revised accordingly.
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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