## Class ten Maths chap 3 NCERT Solutions

**Chapter 3: Pair of Linear Equations in Two Variables**

**TEXTBOOK’S EXERCISE 3.2 **

**1. Form the pair of linear equations in the following problems, and find their solutions graphically. **

(i) **10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. **

(**ii) 5 pencils and 7 pens 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. **

**Sol. **(i) Let number of boys in the quiz = x and number of girls = y

∴ x + y = 10

x + y = 10 – 0 …(i)

As per condition,

y = x + 4 ⇒ x – y = – 4 …(ii)

From (i) y = 10 – x

Points are D (10, 0), E(3, 7) and F(0, 10).

From (ii) y = x + 4

Points are A (– 4, 0), B(0, 4), E(3, 7). We plot these points on a graph paper and draw the lines DF and AB representing x + y = 10 and x – y = – 4 respectively as shown below.

From the graph, it clear that both the linear equations intersect at a point E (3, 7). So, point

E (3, 7) is the solution.

Hence, number of boys in the quiz = 3,

number of girls in the quiz = 7

(ii) Let cost of one pencil = ` x

Cost of one pen = ` y

**Case
I : **As per condition,

5x + 7y = 50 …(i)

**Case
II : **As per condition,

7x + 5y = 46 …(ii)

From equation (i), we have 5x + 7y = 50

Plotting the points U (10, 0), V (3, 5), W(– 4, 10) and drawing a line joining them we get the graph of equation.

5x + 7y = 50

From (ii), 7x + 5y = 46

Plotting the points P(0, 9.2), V(3, 5),R (8, –2) and drawing a line joining them we get the graph of equation 7x +5y = 46.

From the graph, it is clear that both the lines intersect at a point V (3, 5).

So, point V(3, 5) is the solution.

Hence, the cost of one pencil = Rs 3, and the cost of one pen = Rs 5.

**Sol.
**(i) Given equations are :

5x – 4y + 8 = 0 …(i)

7x + 6y – 9 = 0

Hence, given pair of linear equations intersect at a point.

(ii) Given equations are :

9x + 6y + 24 = 0

18x + 6y + 24 = 0

9x + 6y + 24 = 0

18x + 6y + 24 = 0

Here, a_{1}=9, b_{1}= 3, c_{1}=12 and a_{2}=18, b_{2}=6, c_{2}=24

Hence, given pair of linear equations is coincident.

(iii) Given equations are:

6x – 3y + 10 = 0

2x – y + 9 = 0

Hence, given pair of linear equations are parallel to each other.

**3. On comparing the ratios a**_{1}**/a**_{2}**, b**_{1}**/b**_{2}** and c**_{1}**/c**_{2}**, find out whether the following pair of linear equations are consistent, or inconsistent.**

(i) 3x +2y = 5, 2x – 3y = 7

(ii) 2x – 3y = 8, 4x – 6y = 9

**Sol. **(i) Given equations are :

3x + 2y = 5

Or,

3x + 2y – 5 = 0

2x – 3y = 7

Or, 2x – 3y – 7 = 0

Here, a_{1} = 3, b_{1}= 2, c_{1} = -5

Hence, given pair of linear equations is consistent.

(ii) Given equations are :

2x – 3y = 8 or 2x – 3y – 8= 0———(i)

4x – 6y= 9 or 4x – 6y – 9=0———–(ii)

Hence, given pair of linear equations is inconsistent.

(iii) Given equations are :

Hence, g

5x -3y =11

Or, 5x -3y – 11=0

-10x +6y = – 22

Or, -10x +6y + 22 = 0

Here, a_{1}=
5, b_{1}= -3, c_{1} = -11

And a_{2}=
-10, b_{2}= 6, c_{2} = 22

iven pair of linear equations is consistent.

(iv) Given equations are :

Hence, given pair of linear equations is consistent.

Hence, a given pair of linear equations is consistent.