If the graphs of the equations \(3x+ay=22\) and \(x+y=7\) intersect at \(\left(4,3\right)\), what is the value of \(a\)?
Answer and explanation
Correct answer: \(\frac{10}{3}\)
The intersection point \(\left(4,3\right)\) satisfies both equations. Substituting \(x=4\) and \(y=3\) into the first equation gives \(3(4)+a(3)=22\), or \(12+3a=22\). Thus, \(3a=10\), so \(a=\frac{10}{3}\). Option D results from dividing \(22\) by \(3\) without first subtracting the \(12\) contributed by \(3x\). Exam tip: Substitute the coordinates of the graphical intersection point into the equation containing the unknown parameter.
Frequently asked questions
What is the correct answer to this question?
\(\frac{10}{3}\)
Why is this the correct answer?
The intersection point \(\left(4,3\right)\) satisfies both equations. Substituting \(x=4\) and \(y=3\) into the first equation gives \(3(4)+a(3)=22\), or \(12+3a=22\). Thus, \(3a=10\), so \(a=\frac{10}{3}\). Option D results from dividing \(22\) by \(3\) without first subtracting the \(12\) contributed by \(3x\). Exam tip: Substitute the coordinates of the graphical intersection point into the equation containing the unknown parameter.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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