After simplifying and solving \(\frac{x}{4}+\frac{y}{5}=6\) and \(\frac{x}{5}-\frac{y}{4}=1\), what is \(x\)?
Answer and explanation
Correct answer: 20
Multiplying the first equation by 20 gives \(5x+4y=120\), and multiplying the second by 20 gives \(4x-5y=20\). Multiply these equations by 5 and 4 respectively, then add them: \(41x=820\). Hence, \(x=20\). The nearby option \(18\) is incorrect because it does not satisfy both original equations. 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?
20
Why is this the correct answer?
Multiplying the first equation by 20 gives \(5x+4y=120\), and multiplying the second by 20 gives \(4x-5y=20\). Multiply these equations by 5 and 4 respectively, then add them: \(41x=820\). Hence, \(x=20\). The nearby option \(18\) is incorrect because it does not satisfy both original equations. 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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