Draw the graph for each of the equation x + y = 6 and x – y = 2
Draw the graph for each of the equation x + y = 6 and x – y = 2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.
$x+y=6$
$\Rightarrow y=-x+6$
When $x=0, y=-0+6=6$
When $x=1, y=-1+6=5$
When $x=3, y=-3+6=3$
Thus, the points on the line x + y = 6 are as given in the following table:
Plotting the points (0, 6), (1, 5) and (3, 3) and drawing a line passing through these points, we obtain the graph of of the line x + y = 6.
$x-y=2$
$\Rightarrow y=x-2$
When $x=0, y=0-2=-2$
When $x=2, y=2-2=0$
When $x=-1, y=-1-2=-3$
Thus, the points on the line x – y = 2 are as given in the following table:
Plotting the points (0, –2), (2, 0) and (–1, –3) and drawing a line passing through these points, we obtain the graph of of the line x – y = 2.
It can be seen that the lines x + y = 6 and x – y = 2 intersect at the point (4, 2).
Frequently Asked Questions
Find answers to common questions.
What does it mean when two linear equations have no intersection point on a graph?
When two lines do not intersect, they are parallel — they have the same slope but different y-intercepts. This means the pair of linear equations has no solution. For example, x + y = 6 and x + y = 4 are parallel lines and will never meet on the Cartesian plane.
How many points do I need to plot a straight line on a graph?
Mathematically, you only need two points to define a straight line. However, for exam accuracy and error-checking, always calculate and plot three points. If all three are collinear (fall on the same straight line), your table of values is correct. If they are not, recheck your substitution.
What are the coordinates of the point where x + y = 6 and x – y = 2 intersect?
The two lines x + y = 6 and x – y = 2 intersect at the point (4, 2). This means x = 4 and y = 2 satisfies both equations simultaneously. You can verify: 4 + 2 = 6 ✓ and 4 – 2 = 2 ✓. Graphically, this is the point where the two straight lines cross on the Cartesian plane.
Why is the graphical method important for JEE Foundation students?
The graphical method builds coordinate geometry intuition — understanding how equations map to lines, how slopes affect direction, and what intersection means geometrically. These ideas extend directly to JEE Main and Advanced topics like straight lines, circles, and conic sections. Students at eSaral, taught by IIT Bombay faculty ( AIR-41 rankers), are shown these connections from Class 9 itself so that advanced concepts feel natural later.
What chapter is this question from in the NCERT syllabus?
This question is from NCERT Class 9 Mathematics, Chapter 4 — Linear Equations in Two Variables. It also connects to Class 10 Chapter 3 (Pair of Linear Equations in Two Variables), where graphical, substitution, and elimination methods are all covered formally. For full chapter-wise solutions, visit eSaral's NCERT Solutions for Class 11 Maths for more advanced linear equation problems.
Can I solve x + y = 6 and x – y = 2 without drawing a graph?
Yes. You can use the elimination method (add the equations to eliminate y: 2x = 8, so x = 4, then y = 2) or the substitution method. However, the graphical method is specifically required in NCERT Class 9, Chapter 4, because it builds visual understanding of what a "solution" to a pair of linear equations truly means.