Solving 0.25x + y = 9 and x - 0.5y = 2, what is the value of y?
Answer and explanation
Correct answer: 68/9
The governing idea is elimination after converting decimal coefficients into whole-number coefficients. Multiplying 0.25x + y = 9 by 4 gives x + 4y = 36. Multiplying x - 0.5y = 2 by 2 gives 2x - y = 4. From the second equation, x = 2 + y/2. Substituting this into the first gives 2 + y/2 + 4y = 36, so 9y/2 = 34 and y = 68/9. Hence option C is correct. The integer choices 6, 7, and 9 do not satisfy both original equations; substituting y = 8, for example, would also fail because the resulting x values disagree.
Frequently asked questions
What is the correct answer to this question?
68/9
Why is this the correct answer?
The governing idea is elimination after converting decimal coefficients into whole-number coefficients. Multiplying 0.25x + y = 9 by 4 gives x + 4y = 36. Multiplying x - 0.5y = 2 by 2 gives 2x - y = 4. From the second equation, x = 2 + y/2. Substituting this into the first gives 2 + y/2 + 4y = 36, so 9y/2 = 34 and y = 68/9. Hence option C is correct. The integer choices 6, 7, and 9 do not satisfy both original equations; substituting y = 8, for example, would also fail because the resulting x values disagree.
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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