# NCERT solutions for class 10 maths chapter 3 part 1

In this page NCERT solutions for class 10 maths chapter 3 part 1 you can find solutions for exercise problems.

## NCERT solutions for class 10 maths chapter 3 part 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.

Solution:

Total number of students in the class = 10

Let “x” be the number of boys

Let “y” be the number of girls

Number of girls is 4 more than the number of boys

y = x + 4

x – y = - 4 -----(1)

Total number of boys + number of girls = 10

x + y = 10  -----(2)

y = 10 – x

So far we have formed two equations from the above given information. Now we need to make a graph. The two are intersecting at the point (3,7). Here 3 is representing the value of x and 7 is representing the value of y.

Therefore the number of boys = 3

Number of girls = 7

(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.

Solution:

Let “x” be the cost of one pencil

Let “y” be the cost of one pen

5 x + 7 y = 50 -------(1)

7 x + 5 y = 46 -------(2) The two are intersecting at the point (3,5). Here 3 is representing the value of x and 7 is representing the value of y.

Therefore cost of one pencil = 3

Cost of one pen = 5

(2) On comparing the ratios a₁/a₂, b₁/b₂, c₁/c₂, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.

 (i)  5 x – 4 y + 8 = 0      7 x + 6 y – 9 = 0 (ii)  9 x + 3 y + 12 = 0       18 x + 6 y + 24 = 0 (iii)  6 x - 3 y + 10 = 0        2 x - y + 9 = 0 Solution