If the lines \(x+ay=10\) and \(2x-y=5\) intersect at the point \((3,1)\), what is the value of \(a\)?
Advertisement
Answer and explanation
Correct answer: 7
The intersection point \((3,1)\) lies on both lines. Substituting \(x=3\) and \(y=1\) into the first line gives \(3+a(1)=10\), so \(a=7\). The second equation also checks correctly: \(2(3)-1=5\). Exam tip: Substitute the given point into the equation containing the unknown parameter.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The intersection point \((3,1)\) lies on both lines. Substituting \(x=3\) and \(y=1\) into the first line gives \(3+a(1)=10\), so \(a=7\). The second equation also checks correctly: \(2(3)-1=5\). Exam tip: Substitute the given 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..
Advertisement