For 14x + 5y = 77 and 7x - 5y = -7, what is the value of y - x in the solution?
Answer and explanation
Correct answer: 41/15
Add the two equations because the y coefficients are opposites: (14x + 5y) + (7x - 5y) = 77 - 7. This gives 21x = 70 and x = 10/3. Substitute into 14x + 5y = 77: 14(10/3) + 5y = 77, so 140/3 + 5y = 231/3 and 5y = 91/3. Hence y = 91/15. Now calculate y - x = 91/15 - 10/3 = 91/15 - 50/15 = 41/15. Therefore option C is correct. The original integer options do not contain the exact result, so selecting 5, 6, or 8 would be mathematically unjustified.
Frequently asked questions
What is the correct answer to this question?
41/15
Why is this the correct answer?
Add the two equations because the y coefficients are opposites: (14x + 5y) + (7x - 5y) = 77 - 7. This gives 21x = 70 and x = 10/3. Substitute into 14x + 5y = 77: 14(10/3) + 5y = 77, so 140/3 + 5y = 231/3 and 5y = 91/3. Hence y = 91/15. Now calculate y - x = 91/15 - 10/3 = 91/15 - 50/15 = 41/15. Therefore option C is correct. The original integer options do not contain the exact result, so selecting 5, 6, or 8 would be mathematically unjustified.
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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