When the equations \(3x-2y=4\) and \(x+5y=23\) are represented graphically, which is their point of intersection, i.e. their graphical solution?
Answer and explanation
Correct answer: Point \(\left(\frac{66}{17},\frac{65}{17}\right)\)
From the second equation, \(x=23-5y\). Substituting this into the first equation gives \(3(23-5y)-2y=4\), or \(69-17y=4\), so \(y=\frac{65}{17}\). Therefore, \(x=23-5\left(\frac{65}{17}\right)=\frac{66}{17}\). Hence, the two lines intersect at \(\left(\frac{66}{17},\frac{65}{17}\right)\). In option B, the value of \(x\) is incorrect. Exam tip: The graphical solution is the common point of the two lines; verify the point by substituting it into both equations.
Frequently asked questions
What is the correct answer to this question?
Point \(\left(\frac{66}{17},\frac{65}{17}\right)\)
Why is this the correct answer?
From the second equation, \(x=23-5y\). Substituting this into the first equation gives \(3(23-5y)-2y=4\), or \(69-17y=4\), so \(y=\frac{65}{17}\). Therefore, \(x=23-5\left(\frac{65}{17}\right)=\frac{66}{17}\). Hence, the two lines intersect at \(\left(\frac{66}{17},\frac{65}{17}\right)\). In option B, the value of \(x\) is incorrect. Exam tip: The graphical solution is the common point of the two lines; verify the point by substituting it into 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..
