# Linear Equations In Two Variables MCQ CBSE Class 10

This online Maths quiz comprises various multiple choice questions based on the chapter a pair of linear equations in two variables, which is in the syllabus of CBSE Class 10 Maths. NCERT book for maths is generally considered best for the preperation of boards for CBSE class X maths.

## Linear Equation in Two Variables

It is a type of equation that is in the form ax + by + c = 0, where a, b and c are constants and a and b are non zero. Example: 3x + 4y = 5
When two such linear equations in two variables are given, then the solution of the given equations may come.
The solution is the values of x and y which satisfy the given equation.
The number of solutions depends upon the relationship between the graphs of the two linear equations in two variables.

## Relationship between a pair of linear equation in two variables:

### 1. Consistent pair of linear equations in two variables

Consistent pair of linear equations have solutions. They are further divided into two types.

#### a. Coincident pair of lines:

These two lines coincide with each other i.e. they lie on each other. This pair of lines has infinitely many solutions.

#### b. Intersecting lines:

If two lines intersect each other, they will meet on any one point. That is why this pair of linear equations has a unique solution.

### 2. Inconsistent pair of linear equations in two variables

If a pair of lines are parallel to each other, they will never meet. It means that they will never have any solution. So, inconsistent pairs of linear equations have no solution.

## Methods of solving linear equations in two variables

### 1. Substitution Method:

In this method, the following procedure is used:

(i) Solve one of the given equations by taking out a value of one variable in terms of the other.
(ii) Substitute the value of the variable in the second equation.
(iii) Now solve this equation which has taken the form of a linear equation in one variable.
(iv) Once you find the value of one variable in step (iii), but that value in any of the given equations to find the value of the other variable.

### 2. Elimination method

To find the solution of a given pair of linear equations in two variables by this method, we follow the following procedure.

(i) Make sure that both the equations are in the form ax + by + c = 0. If not, then change their form.
(ii) Equate the coefficients of any one variable of both the equations bu multiplying the two equations with the same or different numbers.
(iii) Now add or subtract both the equations to eliminate the variable with the same coefficients.
(iv) Now, solve the remaining equation which is in the form of linear equation in one variable.
(v) Put the value of the variable found in step (iii) in any of the given equations to find the value of the other variable.

### 3. Cross-multiplication method

In this method, it is very important to consider both the equations in the general form:

We take the coefficients of x and y and the value of c from each of the equations to make a formula.

With the above formula we solve the equations and find the value of the two variables.
If you want to go through the chapter again or want to know how to solve the sums on A pair of Linear Equations In Two Variables CBSE Class 10 Maths, you can follow the link given below for video tutorial of the chapter 'A pair of Linear equations in two variables'.

## Linear Equations In Two Variables MCQ CBSE Class 10

Now as you are ready to attempt these multiple-choice questions from this online quiz, please go through the rules first.

## Rules For The Quiz:

• This quiz has 10 multiple-choice questions.
• Each sum has 5 marks.
• So the maximum marks are 50.
• There is no time limit.
• You should be ready with a pen and copy in your hand to solve the sums.
• keep your Maths book away from you. This is the test of your memory. So do not take the help of the Maths book.
• The correct answer and explanation are provided at the end of this quiz.

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