If (x=5-y) and (2x+y=8), what will be the value of (y)?
Answer and explanation
Correct answer: \(y=2\)
Given \(x=5-y\), substitute it into \(2x+y=8\): \(2(5-y)+y=8\). This gives \(10-2y+y=8\), or \(10-y=8\). Hence, \(y=2\). If \(y=3\), then \(x=2\) and \(2x+y=7\), so it does not satisfy the given equation. Exam tip: while expanding after substitution, write the negative term \(-2y\) carefully.
Frequently asked questions
What is the correct answer to this question?
\(y=2\)
Why is this the correct answer?
Given \(x=5-y\), substitute it into \(2x+y=8\): \(2(5-y)+y=8\). This gives \(10-2y+y=8\), or \(10-y=8\). Hence, \(y=2\). If \(y=3\), then \(x=2\) and \(2x+y=7\), so it does not satisfy the given equation. Exam tip: while expanding after substitution, write the negative term \(-2y\) carefully.
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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