What is the solution of (y=2x) and (x+y=12)?
Answer and explanation
Correct answer: \((4,8)\)
Using substitution, the first equation gives \(y=2x\). Substituting it into \(x+y=12\) gives \(x+2x=12\), so \(3x=12\). Hence \(x=4\) and \(y=8\), making \((4,8)\) the solution. Although \((6,6)\) satisfies the second equation, it does not satisfy \(y=2x\). Exam tip: verify the ordered pair in both equations.
Frequently asked questions
What is the correct answer to this question?
\((4,8)\)
Why is this the correct answer?
Using substitution, the first equation gives \(y=2x\). Substituting it into \(x+y=12\) gives \(x+2x=12\), so \(3x=12\). Hence \(x=4\) and \(y=8\), making \((4,8)\) the solution. Although \((6,6)\) satisfies the second equation, it does not satisfy \(y=2x\). Exam tip: verify the ordered pair in 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..
