At which point do the lines \(2x+y=11\) and \(x+y=8\) intersect on the graph?
Answer and explanation
Correct answer: \((3,5)\)
Subtracting the second equation from the first gives \(x=3\). Substituting this into \(x+y=8\) gives \(y=5\). Therefore, the intersection point is \((3,5)\). Check: \(2(3)+5=11\) and \(3+5=8\). In the graphical method, the common point of the two lines represents the solution of the pair. Exam tip: verify both coordinates in both equations.
Frequently asked questions
What is the correct answer to this question?
\((3,5)\)
Why is this the correct answer?
Subtracting the second equation from the first gives \(x=3\). Substituting this into \(x+y=8\) gives \(y=5\). Therefore, the intersection point is \((3,5)\). Check: \(2(3)+5=11\) and \(3+5=8\). In the graphical method, the common point of the two lines represents the solution of the pair. Exam tip: verify both coordinates 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..
