What is the value of (y) from (\frac{2x-3y}{5}=1) and (\frac{x+y}{2}=6)?
Answer and explanation
Correct answer: \(\frac{19}{5}\)
Multiplying the first equation by 5 gives \(2x-3y=5\), and multiplying the second equation by 2 gives \(x+y=12\). From \(x+y=12\), write \(x=12-y\). Substituting gives \(2(12-y)-3y=5\), so \(24-5y=5\). Hence, \(-5y=-19\) and \(y=\frac{19}{5}\). The nearby distractor \(\frac{21}{5}\) does not satisfy both equations together. Exam tip: In linear equations containing fractions, first clear the denominators by multiplying both sides appropriately.
Frequently asked questions
What is the correct answer to this question?
\(\frac{19}{5}\)
Why is this the correct answer?
Multiplying the first equation by 5 gives \(2x-3y=5\), and multiplying the second equation by 2 gives \(x+y=12\). From \(x+y=12\), write \(x=12-y\). Substituting gives \(2(12-y)-3y=5\), so \(24-5y=5\). Hence, \(-5y=-19\) and \(y=\frac{19}{5}\). The nearby distractor \(\frac{21}{5}\) does not satisfy both equations together. Exam tip: In linear equations containing fractions, first clear the denominators by multiplying both sides appropriately.
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..
