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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

——————–4

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, a1=9, b1= 3, c1=12 and a2=18, b2=6, c2=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 a1/a2, b1/b2 and c1/c2, 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, a1 = 3, b1= 2, c1 = -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, a1= 5, b1= -3, c1 = -11

And a2= -10, b2= 6, c2 = 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.

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