Ncert mathematics solutions class 9 Solutions for Chapter 4 linear equations in two variables

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y)

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, and c in each case:

\text { (i) } 2 x+3 y=9.3 \overline{5}

\text { (ii) } x-\frac{y}{5}-10=0

(iii) –2x + 3y = 6

(iv) x = 3y

(v) 2x = –5y

(vi) 3x + 2 = 0

(vii) y – 2 = 0

(viii) 5 = 2x

Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

Which one of the following options is true, and why?

y = 3x + 5 has

(i) A unique solution

(ii) Only two solutions

(iii) Infinitely many solutions

Write four solutions for each of the following equations:

(i) 2x + y = 7

\text { (ii) } \pi x+y=9

(iii) x = 4y

Check which of the following are solutions of the equation x – 2y = 4 and which are not:

(i) (0, 2)

(ii) (2, 0)

(iii) (4, 0)

(iv) (√2, 4√2)

(v) (1, 1)

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

The taxi fare in a city is as follows: For the first kilometer, the fare is ₹ 8 and for the subsequent distance it is ₹5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information, and draw its graph.

From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7.

For Fig. 4. 6

(i) y = x

(ii) x + y = 0

(iii) y = 2x

(iv) 2 + 3y = 7x

For Fig. 4. 7

(i) y = x + 2

(ii) y = x – 2

(iii) y = –x + 2

(iv) x + 2y = 6