Which is the correct solution of (11x+4y=68) and (7x-4y=4)?
Answer and explanation
Correct answer: \((x,y)=(4,6)\)
Adding the two equations gives \((11x+4y)+(7x-4y)=68+4\), so \(18x=72\). Hence, \(x=4\). Substituting \(x=4\) into \(7x-4y=4\) gives \(28-4y=4\), and therefore \(y=6\). Thus, the correct solution is \((4,6)\). In option A, substituting \(x=3\) does not satisfy the second equation. Exam tip: When the coefficients of one variable are opposites, add the equations to eliminate that variable directly.
Frequently asked questions
What is the correct answer to this question?
\((x,y)=(4,6)\)
Why is this the correct answer?
Adding the two equations gives \((11x+4y)+(7x-4y)=68+4\), so \(18x=72\). Hence, \(x=4\). Substituting \(x=4\) into \(7x-4y=4\) gives \(28-4y=4\), and therefore \(y=6\). Thus, the correct solution is \((4,6)\). In option A, substituting \(x=3\) does not satisfy the second equation. Exam tip: When the coefficients of one variable are opposites, add the equations to eliminate that variable directly.
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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