OP Malhotra Notes on Coordinates and Graphs of Simultaneous Linear Equations Class-9 S.Chand ICSE Maths 2026-27. We Provide Step by Step Notes on Linear Equation In One Variable Graph, Distance Between Two Graphs, etc. with Chapter Test of OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-9.

OP Malhotra Coordinates and Graphs of Simultaneous Linear Equations Class-9 S.Chand ICSE Maths Ch-20

Linear Equations :

The equation of a straight line is the linear equation. It could be in one variable or two variables.

Linear Equation in One Variable

The equation with one variable in it is known as a Linear Equation in One Variable.
The general form is
px + q = s, where p, q and s are real numbers and p ≠ 0.
Example : x + 5 = 10
y – 3 = 19
These are called Linear Equations in One Variable because the highest degree of the variable is one.

Practice Questions on Linear Equation :- Exercise-20(a)

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Graph of the Linear Equation in One Variable :

We can mark the point of the linear equation in one variable on the number line.

Solution of a Linear Equation :

• There is only one solution in the linear equation in one variable but there are infinitely many solutions in the linear equation in two variables.
• As there are two variables, the solution will be in the form of an ordered pair, i.e. (x, y).
• The pair which satisfies the equation is the solution of that particular equation.

Practice Questions on Graph of Linear Equation In One Variable :- Exercise-20(b)

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How to solve a pair of simultaneous equations graphically?

In order to solve a pair of simultaneous equations graphically, we first draw the graph of the two equations simultaneously. We get two straight lines intersecting each other at a common point. This common point intersection of two lines gives the solution of the pair of simultaneous equations.

Step by Step Process: 

• Rearrange the equations: Express both equations in standard slope-intercept form (y = mx + c).
• Find coordinate points: Calculate at least two (x, y) pairs for each equation by plugging in random (x) values.
• Draw the grid: Set up an (x)-axis and (y)-axis on graph paper with an even, clear scale.
• Plot the lines: Mark the coordinate points for the first equation and connect them with a straight line, then repeat for the second equation.
• Identify the intersection: Locate the exact point where the two straight lines cross each other.
• Read the solution: Note the (x)-coordinate and (y)-coordinate of this intersection point (x, y).
• Verify your answer: Substitute these (x) and (y) values back into your original equations to ensure they work

Practice Questions on Solving Simultaneous Linear Equation :- Exercise-20(c)

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Graphical representation of a linear equation in 2 variables :

• Any linear equation in the standard form ax+by+c=0 has a pair of solutions in the form (x,y), that can be represented in the coordinate plane.
• When an equation is represented graphically, it is a straight line that may or may not cut the coordinate axes.

Calculate Distance Between Two Graphs

We know that distance between two points P (x1 y1) and Q (x2, y2)
= √[(x2−x1)²+(y2−y1)²].

Practice Questions on Distance Between Two Graphs :- Exercise-20(d)

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In this chapter, we study all the topics on Coordinates and Graphs of Simultaneous Linear Equations like Linear Equation In One Variable Graph, Distance Between Two Graphs, etc. and do some practice questions also. Here we solve extra practice questions on this chapter for better understanding.

For extra practice questions on Coordinates and Graphs :- Chapter Test

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— : End of Coordinates and Graphs of Simultaneous Linear Equations OP Malhotra S Chand Solutions :–

Return to :–   OP Malhotra S Chand Solutions for ICSE Class-9 Maths

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