If the point of intersection of the lines \(2x+ay=16\) and \(x+y=7\) is \((2,5)\), what is the value of \(a\)?
Answer and explanation
Correct answer: \(\frac{12}{5}\)
The intersection point \((2,5)\) is a common solution of both lines. Substituting \(x=2\) and \(y=5\) in the first equation gives \(2(2)+a(5)=16\), or \(4+5a=16\). Hence, \(5a=12\) and \(a=\frac{12}{5}\). Option A is incorrect because it makes the left-hand side equal to \(14\), not \(16\). Exam tip: When a graphical solution is given, substitute the point into both equations to verify it.
Frequently asked questions
What is the correct answer to this question?
\(\frac{12}{5}\)
Why is this the correct answer?
The intersection point \((2,5)\) is a common solution of both lines. Substituting \(x=2\) and \(y=5\) in the first equation gives \(2(2)+a(5)=16\), or \(4+5a=16\). Hence, \(5a=12\) and \(a=\frac{12}{5}\). Option A is incorrect because it makes the left-hand side equal to \(14\), not \(16\). Exam tip: When a graphical solution is given, substitute the point into both equations to verify it.
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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