What is the intersection point of the graphs of \\(2x+y=7\\) and \\(x+y=5\\)?
Answer and explanation
Correct answer: \\(2,3\\)
Subtracting the second equation from the first gives \\(x=2\\). Substituting this into \\(x+y=5\\) gives \\(y=3\\). Therefore, the intersection point is \\(2,3\\). For example, option B gives \\(2(3)+2=8\\), so it does not satisfy the first equation. Exam tip: verify a graphical-solution point in both equations.
Frequently asked questions
What is the correct answer to this question?
\\(2,3\\)
Why is this the correct answer?
Subtracting the second equation from the first gives \\(x=2\\). Substituting this into \\(x+y=5\\) gives \\(y=3\\). Therefore, the intersection point is \\(2,3\\). For example, option B gives \\(2(3)+2=8\\), so it does not satisfy the first equation. Exam tip: verify a graphical-solution 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..
