notes for ClaSS 10 Pair of Linear Equations download PDF

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NCERT Notes For Class 10 Mathematics

Chapter 3 : Pair of linear equations in two variables

Main Points

 An equation of the form ax + by + c = 0, where a, b, c are real nos (a  0, b  0) is called a inear equation in two variables x and y.

$Clas11MathCh14notes1$

 The general form for a pair of linear equations in two variables x and y is

 Graphical representation of a pair of linear equations in two variables:

$NCERT Notes For Class 10 Mathematics$

i.e. unique solution. And this type of equations are called consistent pair of linear equations.
Ex: x – 2y = 0
3x + 4y – 20 = 0

$Pair of linear equations in two variables$

(iv) Algebraic methods of solving a pair of linear equations:
(i) Substitution method
(ii) Elimination Method
(iii) Cross multiplication method

Level - 1

$Algebraic methods of solving a pair of linear equation$

$Substitution method$

8. For what value of k the following pair has infinite number of solutions.
(k-3)x + 3y = k
k(x+y)=12
Ans: k= 6

$Elimination Method$

Level - 2

1. 5 pencils and 7pens together cost Rs. 50 whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
Ans: Cost of one pencil = Rs. 3
Cost of one pen = Rs. 5

2. Solve the equations:
3x – y = 3
7x + 2y = 20
Ans: x=2, y=3

3. Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7
when the denominator is increased by 4
Ans: 28/45

4. Solve the equation:
px + qy = p – q
qx – py = p + q
Ans: x = 1, y = -1

Level - 3

1. Solve the equation using the method of substitution:

$Solve the equation using the method of substitution$

3. Solve the equations by using the method of cross multiplication:

4. A man has only 20 paisa coins and 25 paisa coins in his purse, If he has 50 coins in all totaling Rs. 11.25, how many coins of each kind does he have.
Ans. 25 coins of each kind

5. For what value of k, will the system of equations

$For what value of k, will the system of equations$