On solving (0.5x-0.2y=1.9) and (0.3x+0.4y=2.6), what is (y)?
Answer and explanation
Correct answer: \(y=\frac{73}{26}\)
Multiplying both equations by 10 gives \(5x-2y=19\) and \(3x+4y=26\). Multiplying the first equation by 2 gives \(10x-4y=38\). Adding it to the second equation gives \(13x=64\), so \(x=\frac{64}{13}\). Substituting this into \(5x-2y=19\) gives \(y=\frac{73}{26}\). A nearby value such as \(\frac{68}{26}\) can result from an error in elimination or substitution. Exam tip: For linear equations with decimals, first multiply by 10 or 100 to remove the decimals.
Frequently asked questions
What is the correct answer to this question?
\(y=\frac{73}{26}\)
Why is this the correct answer?
Multiplying both equations by 10 gives \(5x-2y=19\) and \(3x+4y=26\). Multiplying the first equation by 2 gives \(10x-4y=38\). Adding it to the second equation gives \(13x=64\), so \(x=\frac{64}{13}\). Substituting this into \(5x-2y=19\) gives \(y=\frac{73}{26}\). A nearby value such as \(\frac{68}{26}\) can result from an error in elimination or substitution. Exam tip: For linear equations with decimals, first multiply by 10 or 100 to remove the decimals.
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..
