If (4x+7y=1) and (8x-7y=35), which ordered pair of (x) and (y) is correct?
Answer and explanation
Correct answer: \((3,-\frac{11}{7})\)
Adding the two equations gives \((4x+7y)+(8x-7y)=1+35\), so \(12x=36\). Hence, \(x=3\). Substituting \(x=3\) into \(4x+7y=1\) gives \(12+7y=1\), so \(7y=-11\) and \(y=-\frac{11}{7}\). Therefore, the correct ordered pair is \((3,-\frac{11}{7})\). Option B does not satisfy both equations when \(x=2\). Exam tip: When coefficients of one variable have opposite signs, add the equations to eliminate that variable quickly.
Frequently asked questions
What is the correct answer to this question?
\((3,-\frac{11}{7})\)
Why is this the correct answer?
Adding the two equations gives \((4x+7y)+(8x-7y)=1+35\), so \(12x=36\). Hence, \(x=3\). Substituting \(x=3\) into \(4x+7y=1\) gives \(12+7y=1\), so \(7y=-11\) and \(y=-\frac{11}{7}\). Therefore, the correct ordered pair is \((3,-\frac{11}{7})\). Option B does not satisfy both equations when \(x=2\). Exam tip: When coefficients of one variable have opposite signs, add the equations to eliminate that variable quickly.
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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