In 13x−6y=1 and 13x+9y=61, what is the value of y?
Answer and explanation
Correct answer: 4
Because the coefficients of x are equal in both equations, subtract the first equation from the second. This gives (13x + 9y) − (13x − 6y) = 61 − 1. The x terms cancel and 15y = 60 remains. Dividing by 15 gives y = 4, so option C is correct. We can verify the associated x-value: substituting y = 4 into 13x − 6y = 1 gives 13x − 24 = 1, hence 13x = 25 and x = 25/13. The second equation then gives 25 + 36 = 61, confirming consistency. The other options would make the difference of the equations equal to 30, 45 or 75 rather than 60, so they cannot satisfy both equations.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Because the coefficients of x are equal in both equations, subtract the first equation from the second. This gives (13x + 9y) − (13x − 6y) = 61 − 1. The x terms cancel and 15y = 60 remains. Dividing by 15 gives y = 4, so option C is correct. We can verify the associated x-value: substituting y = 4 into 13x − 6y = 1 gives 13x − 24 = 1, hence 13x = 25 and x = 25/13. The second equation then gives 25 + 36 = 61, confirming consistency. The other options would make the difference of the equations equal to 30, 45 or 75 rather than 60, so they cannot satisfy both equations.
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.
