Find the value of (y) from (2x+3y=17) and (2x+y=9).
Answer and explanation
Correct answer: (y=4)
The equations are \\(2x+3y=17\\) and \\(2x+y=9\\). Their x-terms are identical, so subtract the second equation from the first: \\((2x+3y)-(2x+y)=17-9\\). The \\(2x\\) terms cancel, leaving \\(2y=8\\). Dividing by 2 gives \\(y=4\\). Therefore option C is correct. This is the elimination method because one variable is removed by subtraction.
Substitution provides a check. From the second equation, \\(2x=9-y\\). With \\(y=4\\), we get \\(2x=5\\), and the first equation becomes \\(5+12=17\\), which is true. The other listed values for y do not satisfy both equations simultaneously. Hence the supplied answer C is consistent and the cancellation step gives the value efficiently.
Frequently asked questions
What is the correct answer to this question?
(y=4)
Why is this the correct answer?
The equations are \\(2x+3y=17\\) and \\(2x+y=9\\). Their x-terms are identical, so subtract the second equation from the first: \\((2x+3y)-(2x+y)=17-9\\). The \\(2x\\) terms cancel, leaving \\(2y=8\\). Dividing by 2 gives \\(y=4\\). Therefore option C is correct. This is the elimination method because one variable is removed by subtraction.
Substitution provides a check. From the second equation, \\(2x=9-y\\). With \\(y=4\\), we get \\(2x=5\\), and the first equation becomes \\(5+12=17\\), which is true. The other listed values for y do not satisfy both equations simultaneously. Hence the supplied answer C is consistent and the cancellation step gives the value efficiently.
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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