If 5(2x−y)−3(x+y)=11 and 2(2x−y)+4(x+y)=50, what is the value of y?
Answer and explanation
Correct answer: 131/39
Introduce u = 2x − y and v = x + y. The given equations then become 5u − 3v = 11 and 2u + 4v = 50. Eliminating v, multiply the first equation by 4 and the second by 3: 20u − 12v = 44 and 6u + 12v = 150. Thus 26u = 194, so u = 97/13. Substitution into 2u + 4v = 50 gives 4v = 50 − 194/13 = 456/13, hence v = 114/13. From u = 2x − y and v = x + y, we have y = (2v − u)/3. Therefore y = [228/13 − 97/13]/3 = 131/39. The original integer options and supplied answer were incorrect, so option A has been corrected to the exact value.
Frequently asked questions
What is the correct answer to this question?
131/39
Why is this the correct answer?
Introduce u = 2x − y and v = x + y. The given equations then become 5u − 3v = 11 and 2u + 4v = 50. Eliminating v, multiply the first equation by 4 and the second by 3: 20u − 12v = 44 and 6u + 12v = 150. Thus 26u = 194, so u = 97/13. Substitution into 2u + 4v = 50 gives 4v = 50 − 194/13 = 456/13, hence v = 114/13. From u = 2x − y and v = x + y, we have y = (2v − u)/3. Therefore y = [228/13 − 97/13]/3 = 131/39. The original integer options and supplied answer were incorrect, so option A has been corrected to the exact value.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
