If x/2 + y/3 = 7 and x/3 + y/2 = 8, what is the value of x + y?
Answer and explanation
Correct answer: 18
First clear the denominators by multiplying each equation by 6. The system becomes 3x + 2y = 42 and 2x + 3y = 48. Adding these equations gives 5x + 5y = 90. Factor out 5: 5(x + y) = 90, and divide by 5 to obtain x + y = 18. There is no need to find x and y separately because the required expression appears directly after addition. For verification, solving gives x = 6 and y = 12, whose sum is also 18. Therefore option B is correct; 17, 19 and 20 do not satisfy the derived sum.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
First clear the denominators by multiplying each equation by 6. The system becomes 3x + 2y = 42 and 2x + 3y = 48. Adding these equations gives 5x + 5y = 90. Factor out 5: 5(x + y) = 90, and divide by 5 to obtain x + y = 18. There is no need to find x and y separately because the required expression appears directly after addition. For verification, solving gives x = 6 and y = 12, whose sum is also 18. Therefore option B is correct; 17, 19 and 20 do not satisfy the derived sum.
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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