What is the point of intersection of the graphs of \(4x-y=9\) and \(2x+3y=23\), that is, their graphical solution?
Answer and explanation
Correct answer: Point: \(\left(\frac{25}{7},\frac{37}{7}\right)\)
From the first equation, \(y=4x-9\). Substituting this in the second equation gives \(2x+3(4x-9)=23\), so \(14x=50\) and \(x=\frac{25}{7}\). Therefore, \(y=4\left(\frac{25}{7}\right)-9=\frac{37}{7}\). Hence, the intersection point of the two lines is \(\left(\frac{25}{7},\frac{37}{7}\right)\). In option B, the coordinates are interchanged, so the point does not satisfy the equations. Exam tip: Always substitute the intersection point into both original equations to verify it.
Frequently asked questions
What is the correct answer to this question?
Point: \(\left(\frac{25}{7},\frac{37}{7}\right)\)
Why is this the correct answer?
From the first equation, \(y=4x-9\). Substituting this in the second equation gives \(2x+3(4x-9)=23\), so \(14x=50\) and \(x=\frac{25}{7}\). Therefore, \(y=4\left(\frac{25}{7}\right)-9=\frac{37}{7}\). Hence, the intersection point of the two lines is \(\left(\frac{25}{7},\frac{37}{7}\right)\). In option B, the coordinates are interchanged, so the point does not satisfy the equations. Exam tip: Always substitute the intersection point into both original equations to verify it.
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..
