## NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables (Ex 4.2) Exercise 4.2

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Q1: What are the Solutions of Linear equation in 2 variables on a graph?

A1: The Solutions of Linear equation in 2 variables on a graph will be :

Any linear equation in the standard form ax+by+c=0 has a pair of solutions (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.

A linear equation ax+by+c=0 is represented graphically as a straight line.

Every point on the line is a solution for the linear equation.

Every solution of the linear equation is a point on the line.

Q2: when do a pair of linear equations with two variables have no solution.

A2: If the two linear equations have equal slope value, then the equations will have no solutions.

m_{1} = m_{2}. This is because the lines are parallel to each other and do not intersect.

Q3: What happens to Linear equation in 2 variables when (i) Lines passing through the origin (ii) Lines parallel to coordinate axes.

A3: In a Linear equation in 2 variables

**(i) Lines Passing Through the Origin**

Certain linear equations exist such that their solution is (0,0). Such equations when represented graphically pass through the origin.

The coordinate axes x-axis and y-axis can be represented as y=0 and x=0 respectively.

**(ii) Lines Parallel to Coordinate Axes**

Linear equations of the form y=a, when represented graphically are lines parallel to the x-axis and a is the y-coordinate of the points in that line.

Linear equations of the form x=a, when represented graphically are lines parallel to the y-axis and a is the x-coordinate of the points in that line.

Q4: How to score well in Algebra?

A4: Algebra is most students' scoring friend. Unlike arithmetic and geometry it does not have any theorems to prove or complicated word problems. Most of the problems in algebra can be solved through logic. Students can develop this logical thinking through repeated practise of algebra problems. Along with this students will have to know basic formulas of algebra and some popular algebraic expressions. All these combined together will help students to score effectively and efficiently high marks in maths. Along with these, students can also refer the follows study materials in order to be able to score well in algebra as well as overall in Maths:

Previous Year Question Papers

Exemplar Solutions

NCERT Solutions

Sample Papers

All the above study materials are provided by Vedantu as free PDF for the students to download. These study resources are curated keeping in mind the need for the students to understand maths rather than just mugging it up.