If \(3x+4y=26\) and \(5x-2y=22\), what is the value of (2x+y)?
Answer and explanation
Correct answer: \(\frac{172}{13}\)
The equations are \(3x+4y=26\) and \(5x-2y=22\). Multiplying the second equation by 2 gives \(10x-4y=44\). Adding it to the first equation eliminates \(y\): \(13x=70\), so \(x=\frac{70}{13}\). Substituting this into the second equation gives \(y=\frac{32}{13}\). Therefore, \(2x+y=2\left(\frac{70}{13}\right)+\frac{32}{13}=\frac{172}{13}\). Hence, option D is correct. Exam tip: Substitute the calculated values back into both original equations to verify the solution.
Frequently asked questions
What is the correct answer to this question?
\(\frac{172}{13}\)
Why is this the correct answer?
The equations are \(3x+4y=26\) and \(5x-2y=22\). Multiplying the second equation by 2 gives \(10x-4y=44\). Adding it to the first equation eliminates \(y\): \(13x=70\), so \(x=\frac{70}{13}\). Substituting this into the second equation gives \(y=\frac{32}{13}\). Therefore, \(2x+y=2\left(\frac{70}{13}\right)+\frac{32}{13}=\frac{172}{13}\). Hence, option D is correct. Exam tip: Substitute the calculated values back into both original equations to verify the solution.
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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