If (x − 1)/2 + (y + 1)/3 = 8 and (x − 1)/3 − (y + 1)/2 = −1, what is the value of x?
Answer and explanation
Correct answer: 145/13
Put u = x − 1 and v = y + 1 to simplify the fractional equations. Multiplying the first equation by 6 gives 3u + 2v = 48, while multiplying the second by 6 gives 2u − 3v = −6. Multiply these equations by 3 and 2 respectively: 9u + 6v = 144 and 4u − 6v = −12. Adding eliminates v and gives 13u = 132, hence u = 132/13. Since x = u + 1, x = 132/13 + 13/13 = 145/13. Thus option A is correct; the original supplied answer and brief explanation incorrectly treated u as 13.
Frequently asked questions
What is the correct answer to this question?
145/13
Why is this the correct answer?
Put u = x − 1 and v = y + 1 to simplify the fractional equations. Multiplying the first equation by 6 gives 3u + 2v = 48, while multiplying the second by 6 gives 2u − 3v = −6. Multiply these equations by 3 and 2 respectively: 9u + 6v = 144 and 4u − 6v = −12. Adding eliminates v and gives 13u = 132, hence u = 132/13. Since x = u + 1, x = 132/13 + 13/13 = 145/13. Thus option A is correct; the original supplied answer and brief explanation incorrectly treated u as 13.
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.
