If (6x+11y=9) and (12x-11y=63), what is the value of (x-y)?
Answer and explanation
Correct answer: \(\frac{59}{11}\)
Adding the two equations eliminates \(y\): \(18x=72\), so \(x=4\). Substituting into \(6x+11y=9\) gives \(24+11y=9\), hence \(y=-\frac{15}{11}\). Therefore, \(x-y=4-\left(-\frac{15}{11}\right)=\frac{59}{11}\). \(\frac{15}{11}\) is only the magnitude of \(y\), not the value of \(x-y\). Exam tip: add equations directly when a variable has opposite coefficients.
Frequently asked questions
What is the correct answer to this question?
\(\frac{59}{11}\)
Why is this the correct answer?
Adding the two equations eliminates \(y\): \(18x=72\), so \(x=4\). Substituting into \(6x+11y=9\) gives \(24+11y=9\), hence \(y=-\frac{15}{11}\). Therefore, \(x-y=4-\left(-\frac{15}{11}\right)=\frac{59}{11}\). \(\frac{15}{11}\) is only the magnitude of \(y\), not the value of \(x-y\). Exam tip: add equations directly when a variable has 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..
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