In 13x - 6y = 8 and 13x + 4y = 48, what is the value of y?
Answer and explanation
Correct answer: 4
The coefficient of x is 13 in both equations, so subtract the first equation from the second to eliminate x. We obtain (13x + 4y) - (13x - 6y) = 48 - 8. Simplifying gives 10y = 40, and division by 10 gives y = 4. A quick check confirms the result: with y = 4, the first equation becomes 13x - 24 = 8, so 13x = 32; the second becomes 13x + 16 = 48, also giving 13x = 32. Thus the equations are consistent and option C is correct. Options 2, 3 and 5 result from incorrect subtraction or division.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The coefficient of x is 13 in both equations, so subtract the first equation from the second to eliminate x. We obtain (13x + 4y) - (13x - 6y) = 48 - 8. Simplifying gives 10y = 40, and division by 10 gives y = 4. A quick check confirms the result: with y = 4, the first equation becomes 13x - 24 = 8, so 13x = 32; the second becomes 13x + 16 = 48, also giving 13x = 32. Thus the equations are consistent and option C is correct. Options 2, 3 and 5 result from incorrect subtraction or division.
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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