Using the graphical method, at which point do the lines \(x+2y=6\) and \(2x+y=6\) intersect?
Answer and explanation
Correct answer: \((2,2)\)
The point of intersection must satisfy both equations. Subtracting the equations gives \(x-y=0\), so \(x=y\). Substituting this in \(x+2y=6\) gives \(3x=6\), hence \(x=y=2\). Therefore, the lines intersect at \((2,2)\). Exam tip: verify a candidate point in both equations; \((4,1)\) satisfies the first equation but not the second.
Frequently asked questions
What is the correct answer to this question?
\((2,2)\)
Why is this the correct answer?
The point of intersection must satisfy both equations. Subtracting the equations gives \(x-y=0\), so \(x=y\). Substituting this in \(x+2y=6\) gives \(3x=6\), hence \(x=y=2\). Therefore, the lines intersect at \((2,2)\). Exam tip: verify a candidate point in both equations; \((4,1)\) satisfies the first equation but not the second.
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..
