For 4x - 9y = 31 and 8x + 9y = 65, what is the value of y in the solution?
Answer and explanation
Correct answer: 1/9
Add the equations because the y-terms, -9y and +9y, cancel: (4x - 9y) + (8x + 9y) = 31 + 65. This gives 12x = 96, so x = 8. Substitute x = 8 into the first equation: 4(8) - 9y = 31, hence 32 - 9y = 31. Therefore -9y = -1 and y = 1/9. Substitution into the second equation also verifies it: 8(8) + 9(1/9) = 64 + 1 = 65. Thus option A is correct. The original listed options did not contain 1/9, so that option was corrected; 1, 2, 3 and 4 would not satisfy both equations for y.
Frequently asked questions
What is the correct answer to this question?
1/9
Why is this the correct answer?
Add the equations because the y-terms, -9y and +9y, cancel: (4x - 9y) + (8x + 9y) = 31 + 65. This gives 12x = 96, so x = 8. Substitute x = 8 into the first equation: 4(8) - 9y = 31, hence 32 - 9y = 31. Therefore -9y = -1 and y = 1/9. Substitution into the second equation also verifies it: 8(8) + 9(1/9) = 64 + 1 = 65. Thus option A is correct. The original listed options did not contain 1/9, so that option was corrected; 1, 2, 3 and 4 would not satisfy both equations for y.
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.
