NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables | Monster Thinks - Monster Thinks

# NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

NCERT Solutions for Class 10 Maths are solved by experts of MonsterThinks.in in order to help students to obtain excellent marks in their board examination. All the questions and answers in the CBSE NCERT Books have been included in this page. We have provided all the Class 10 Maths NCERT Solutions with a detailed explanation i.e., we have solved all the questions with step-by-step solutions in understandable language. So students having great knowledge of NCERT Solutions Class 10 Maths can easily make a grade in their board exams. Read on to find out more about  NCERT Solutions for Class 10 Mathematics.

With the aim of imbibing skills and hard work among the students, the 10th class maths NCERT solutions have been designed. It contains previous years’ questions along with answers except those which are not included in the CBSE 10 maths syllabus.

CBSE NCERT solutions for class 10 maths will help the students in acquiring good practice to do their CBSE Class 10th exam with confidence.

### NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

Pair of Linear Equations Class 10 has a total of seven exercises consisting of 55 Problems. The problems will be based on concepts like linear equations in two variables, algebraic methods for solving linear equations, elimination method, cross-multiplication method Time and Work, Age, Boat Stream and equations reducible to a pair of linear equations these answers will give you ease in solving problems related to linear equations.

### Class 10 Maths Pair of Linear Equations in Two Variables Mind Map

#### System of a Pair of Linear Equations in Two Variables

An equation of the form Ax + By + C = 0 is called a linear equation in two variables x and y where A, B, and C are real numbers.
Two linear equations in the same two variables are called a pair of linear equations in two variables. A standard form of linear equations in two variables.
a1x + b1y + c1 = 0, a2x + b2y + c1 = 0
where a1, a2, b1, b2, c1, c2 are real numbers such that #### Representation of Linear Equation In Two Variables

Every linear equation in two variables graphically represents a line and each solution (x, y) of a linear equation in two variables, ax + by + c = 0, corresponds to a point on the line representing the equation, and vice versa.

#### Plotting Linear Equation in Two Variables on the Graph

There are infinitely many solutions to each linear equation. So, we choose at least any two values of one variable & get the value of other variables by substitution, i.e; Consider; Ax + By + C = 0 We can write the above linear equation as: Here, we can choose any values of x & can find corresponding values of y.
After getting the values of (x, y) we plot them on the graph thereby getting the line representing Ax + By + C = 0.

#### Method of Solution of a Pair of Linear Equations in Two Variables

The Coordinate of the point (x, y) which satisfies the system of pair of linear equations in two variables is the required solution. This is the point where the two lines representing the two equations intersect each other.
There are two methods of finding solutions to a pair of Linear equations in two variables.
(1) Graphical Method: This method is less convenient when the point representing the solution has non-integral coordinates.
(2) Algebraic Method: This method is more convenient when the point representing the solution has non-integral coordinates.
This method is further divided into three methods:
(i) Substitution Method,
(ii) Elimination Method and
(iii) Cross Multiplication Method.

#### Consistency and Nature of the Graphs

Consider the standard form of linear equations in two variables.
a1x + b1y + C1 = 0; a2x + b2y + c2 = 0
While solving the above system of equations following three cases arise.
(i) If; the system is called consistent, having a unique solution and pair of straight lines representing the above equations intersect at one point only
(ii) If; the system is called dependent and has infinitely many solutions. The pair of lines representing the equations coincide.
(iii) If; the system is called inconsistent and has no solution. Pair of lines representing the equations are parallel or do not intersect at any point. #### Algebraic Method of Solution

Consider the following system of equation
a1x + b1y + c1 =0; a2x + b2y + c1 =0
There are the following three methods under the Algebraic method to solve the above system.

##### (i) Substitution method

(a) Find the value of one variable, say y in terms of x or x in terms of y from one equation.
(b) Substitute this value in the second equation to get the equation in one variable and find a solution.
(c) Now substitute the value/solution so obtained in step (b) in the equation got in step (a).

##### (ii) Elimination Method

(a) If the coefficient of any one variable is not the same in both the equations multiply both the equation with suitable non-zero constants to make the coefficient of any one variable numerically equal.
(b) Add or subtract the equations so obtained to get the equation in one variable and solve it.
(c) Now substitute the value of the variable got in the above step in either of the original equation to get the value of the other variable.

#### (iii) Cross multiplication method

For the pair of Linear equations in two variables:
a1x + b1y + C1 = 0
a2x + b2y + c2 = 0
Consider the following diagram. Solve it to get the solution, provided a1b2 – a2b1 ≠ 0

#### Equations Reducible to a Pair of Linear Equations in Two Variables

Sometimes pair of equations are not linear (or not in standard form), then they are altered so that they reduce to a pair of linear equations in standard form.
For example; Here we substitute 1x = p & \frac{1}{y} = q, the above equations reduces to:
a1p + b1q = c1 ; a2p – b2q = c2
Now we can use any method to solve them.