Solving \(\frac{x}{5}-\frac{y}{2}=1\) and \(\frac{x}{2}+\frac{y}{5}=11\), what is the value of \(x\)?
Answer and explanation
Correct answer: \(\frac{570}{29}\)
Multiplying both equations by 10 gives \(2x-5y=10\) and \(5x+2y=110\). Multiply the first equation by 2 and the second by 5 to obtain \(4x-10y=20\) and \(25x+10y=550\). Adding them gives \(29x=570\), so \(x=\frac{570}{29}\). Although \(20\) is a nearby value, it does not satisfy the system. Exam tip: For linear equations containing fractions, first multiply by the LCM to remove the fractions.
Frequently asked questions
What is the correct answer to this question?
\(\frac{570}{29}\)
Why is this the correct answer?
Multiplying both equations by 10 gives \(2x-5y=10\) and \(5x+2y=110\). Multiply the first equation by 2 and the second by 5 to obtain \(4x-10y=20\) and \(25x+10y=550\). Adding them gives \(29x=570\), so \(x=\frac{570}{29}\). Although \(20\) is a nearby value, it does not satisfy the system. Exam tip: For linear equations containing fractions, first multiply by the LCM to remove the fractions.
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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