NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2

# NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2

## NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2

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Ex 3.2 Class 10 Maths Question 1.
Form the pair of linear equations of 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.
Solution:

Ex 3.2 Class 10 Maths Question 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
Solution:

Ex 3.2 Class 10 Maths Question 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 pairs of linear equations are consistent, or inconsistent:
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Solution:

Ex 3.2 Class 10 Maths Question 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
Solution:

Ex 3.2 Class 10 Maths Question 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 graphically.
Solution:

Ex 3.2 Class 10 Maths Question 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
Solution:

Ex 3.2 Class 10 Maths Question 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.
Solution:

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