At which point do the lines \(x+2y=8\) and \(2x+y=10\) intersect on the graph?
Answer and explanation
Correct answer: \((4,2)\)
Substituting the point \((4,2)\) into both equations gives \(4+2(2)=8\) and \(2(4)+2=10\). Therefore, \((4,2)\) is the common point and hence the graphical intersection of the two lines. The nearby option \((3,2)\) is incorrect because it gives \(3+2(2)=7\), not 8, in the first equation. Exam tip: verify an intersection point in both equations.
Frequently asked questions
What is the correct answer to this question?
\((4,2)\)
Why is this the correct answer?
Substituting the point \((4,2)\) into both equations gives \(4+2(2)=8\) and \(2(4)+2=10\). Therefore, \((4,2)\) is the common point and hence the graphical intersection of the two lines. The nearby option \((3,2)\) is incorrect because it gives \(3+2(2)=7\), not 8, in the first equation. Exam tip: verify an intersection point in both equations.
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..
