On solving (8x-3y=31) and (2x+3y=29), what is (y)?
Answer and explanation
Correct answer: \(\frac{17}{3}\)
Adding the two equations eliminates the \(y\)-terms: \((8x-3y)+(2x+3y)=31+29\). Thus, \(10x=60\), so \(x=6\). Substituting this into \(2x+3y=29\) gives \(12+3y=29\), hence \(3y=17\) and \(y=\frac{17}{3}\). The value \(\frac{16}{3}\) does not satisfy the second equation. Exam tip: add equations directly when a variable has equal and opposite coefficients.
Frequently asked questions
What is the correct answer to this question?
\(\frac{17}{3}\)
Why is this the correct answer?
Adding the two equations eliminates the \(y\)-terms: \((8x-3y)+(2x+3y)=31+29\). Thus, \(10x=60\), so \(x=6\). Substituting this into \(2x+3y=29\) gives \(12+3y=29\), hence \(3y=17\) and \(y=\frac{17}{3}\). The value \(\frac{16}{3}\) does not satisfy the second equation. Exam tip: add equations directly when a variable has equal and opposite coefficients.
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..
