**NCERT Solution For Class 10, Maths, Pair Of Linear Equations In Two Variables, Exercise 3.2** includes questions related to day to day examples. Students also needs to find Which of the pairs of linear equations are consistent/inconsistent. If consistent, need to obtain the solution graphically. Class 10, Maths, chapter 3, Exercise 3.2 have total seven questions to discuses.

Table of Contents

Toggle## Class 10, Maths, Chapter 3, Exercise 3.2, Solutions

**Q.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 ****₹**** 50, whereas 7 pencils and 5 pens together cost ****₹ ****46. Find the cost of one pencil and that of one pen.**

**Ans: ****(i) let us denote** the number of girls by ‘x’ and the number of boys by ‘y’.

then, the equations formed are

x + y = 10 eq.(i)

And, x = y + 4

⇒ x – y = 4 eq.(ii)

Let us draw the graphs of equations (i) and (ii) by finding two solutions for each of these equations.

From eq. (i), **x + y = 10 **

When x = 5, y = 5;

when x = 3, y = 7;

Thus, we have the following table:

From eq. (ii), **x – y = 4**

When x = 6, y = 2;

when x = 4, y = 0;

Thus, we have the following table:

Plotting the graph from above tables, we get

These two lines intersect at (**7,3**). So, x = 7 and y = 3 is the required solution.

Hence, the number of girls and boys are 7 and 3 respectively.

**Verification:** Put x = 7 and y = 3 in (i) and (ii), we find that both the equations are satisfied.

**(ii) Let us denote the cost of one pencil by Rs x and one pen by Rs y. Then, the equations formed are**

5x + 7y = 50 eq.(i)

And, 7x + 5y = 46 eq.(ii)

Let us draw the graphs of equations (1) and (2) by finding two solutions for each of these equations. The solutions of the equations are given in table.

5x + 7y = 50

When x = 10, y = 0;

when x = 3, y = 5;

Thus, we have the following table:

**7x + 5y = 46**

When x = 8, y = -2;

when x = 3, y = 5;

Thus, we have the following table:

Plotting the graph from above tables, we get

These two lines intersect at (3, 5). So, x = 3 and y = 5 is the required solution.

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

**Verification:** Put x = 3 and y = 5 in (i) and (ii), wo find that both the equations are satisfied.

**Q.2. On comparing the ratios $\frac{{{a}_{1}}}{{{a}_{2}}},\frac{{{b}_{1}}}{{{b}_{2}}}$and $\frac{{{c}_{1}}}{{{c}_{2}}}$ find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: **

**(i) 5x – 4y + 8 = 0; 7x + 6y – 9 = 0 **

**(ii) 9x + 3y + 12 = 0; 18x + 6y + 24 = 0 **

**(iii) 6x – 3y + 10 = 0; 2x – y + 9 = 0 **

**Ans:**

**Q.3. On comparing ****the ratios $\frac{{{a}_{1}}}{{{a}_{2}}},\frac{{{b}_{1}}}{{{b}_{2}}}$and $\frac{{{c}_{1}}}{{{c}_{2}}}$, 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**

**(iii) **** $\frac{3}{2}x+\frac{5}{3}y=7$; 9x – 10y =14 **

**(iv) 5x – 3y = 11; – 10x + 6y = –22**

**(v) **** $\frac{4}{3}$x + 2y = 8; 2x + 3y =12 **

**Ans:**

**Q.4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:**

**(i) x + y = 5, 2x + 2y = 10**

**(ii) x – y = 8, 3x – 3y = 16**

**(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0**

**(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0**

**Ans:**

**Q.5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.**

**Ans:**

**Q.6. Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:**

**(i) intersecting lines **

**(ii) parallel lines **

**(iii) coincident lines**

**Ans:**

**Q.7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. **

**Ans:**

## NCERT Solutions For Class 10, Maths, Chapter 3, Pair Of Linear Equations In Two Variables (All Exercises)

**Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.1****Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.2****Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.3****Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.4****Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.5****Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.6**