What is the solution of (x=2y+1) and (x+y=13)?
Answer and explanation
Correct answer: (x=9,\ y=4)
One equation already gives x in terms of y: \(x=2y+1\). This makes substitution the natural method. Replace x by \(2y+1\) in the second equation. Then there is only one unknown, y, so it can be found with ordinary algebra. After finding y, substitute it back into the first relation to find x.
Using substitution, \(x+y=13\) becomes \((2y+1)+y=13\). Combine like terms to get \(3y+1=13\), then subtract 1: \(3y=12\). Dividing by 3 gives \(y=4\). Now \(x=2(4)+1=9\). Checking gives \(9+4=13\), so the solution is \((9,4)\), which is option C. The other choices do not satisfy both equations.
Frequently asked questions
What is the correct answer to this question?
(x=9,\ y=4)
Why is this the correct answer?
One equation already gives x in terms of y: \(x=2y+1\). This makes substitution the natural method. Replace x by \(2y+1\) in the second equation. Then there is only one unknown, y, so it can be found with ordinary algebra. After finding y, substitute it back into the first relation to find x.
Using substitution, \(x+y=13\) becomes \((2y+1)+y=13\). Combine like terms to get \(3y+1=13\), then subtract 1: \(3y=12\). Dividing by 3 gives \(y=4\). Now \(x=2(4)+1=9\). Checking gives \(9+4=13\), so the solution is \((9,4)\), which is option C. The other choices do not satisfy both equations.
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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