R s aggarwal solutions mathematics class 9 Solutions for Chapter 4 linear equations in two variables

Exercises in Chapter 4 linear equations in two variables Grade 9

Linear Equations In Two Variables Exercise 4A

Linear Equations In Two Variables Exercise 4B

Questions in Linear Equations In Two Variables Exercise 4A

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

(i) 𝟑𝒙 + 𝟓𝒚 = 𝟕. 𝟓

(ii) 𝟐𝒙 −𝒚/𝟓+ 𝟔 = 𝟎

(iii) 𝟑𝒚 − 𝟐𝒙 = 𝟔

(iv) 𝟒𝒙 = 𝟓𝒚

(v)𝒙/𝟓−𝒚/𝟔= 𝟏

(vi) √𝟐𝒙 + √𝟑𝒚 = 𝟓

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

c in each case.

(i) 𝒙 = 𝟔

(ii) 𝟑𝒙 − 𝒚 = 𝒙 − 𝟏

(iii) 𝟐𝒙 + 𝟗 = 𝟎

(iv) 𝟒𝒚 = 𝟕

(v) 𝒙 + 𝒚 = 𝟒

(vi)𝒙/𝟐−𝒚/𝟑=𝟏/𝟔+ 𝒚

Check which of the following are the solutions of the equation 𝟓𝒙 − 𝟒𝒚 = 𝟐𝟎.

(i) (4, 0)

(ii) (0, 5)

(iii) (-2, 𝟓/𝟐)

(iv) (0, -5)

(v) (2, − 𝟓/𝟐)

Find five different solutions of each of the following equations.

(a) 𝟐𝒙 − 𝟑𝒚 = 𝟔

(b) 𝟐𝒙/𝟓+𝟑𝒚/𝟏𝟎= 𝟑

If x = 3 and y = 4 is a solution of the equation 𝟓𝒙 − 𝟑𝒚 = 𝒌, find the value of k.

If 𝒙 = 𝟑𝒌 + 𝟐 and 𝒚 = 𝟐𝒌 − 𝟏 is a solution of the equation 𝟒𝒙 − 𝟑𝒚 + 𝟏 = 𝟎, find the value of k.

The cost of 5 pencils is equal to the cost of 2 ballpoints. Write a linear equation in two variables to represent this statement. (Take the cost of a pencil to be ₹ x and that of a ballpoint to be ₹ y).

Questions in Linear Equations In Two Variables Exercise 4B

Draw the graph of each of the following equations.

(i) 𝒙 = 𝟒

(ii) 𝒙 + 𝟒 = 𝟎

(iii) 𝒚 = 𝟑

(iv) 𝒚 = −𝟑

(v) 𝒙 = −𝟐

(vi) 𝒙 = 𝟓

(vii) 𝒚 + 𝟓 = 𝟎

(viii) 𝒚 = 𝟒

Draw the graph of the equation 𝒚 = 𝟑𝒙.

From your graph, find the value of y when

(i) 𝒙 = 𝟐

(ii) 𝒙 = −𝟐

Draw the graph of the equation 𝒙 + 𝟐𝒚 − 𝟑 = 𝟎.

From your graph, find the value of y when

(i) 𝒙 = 𝟓

(ii) 𝒙 = −𝟓

Draw the graph of the equation, 𝟐𝒙 − 𝟑𝒚 = 𝟓.

From your graph, find

(i) The value of y when 𝒙 = 𝟒

(ii) The value of x when 𝒚 = 𝟑.

Draw the graph of the equation, 𝟐𝒙 + 𝒚 = 𝟔.

Find the coordinates of the point where the graph cuts the x – axis.

Draw the graph of the equation, 𝟑𝒙 + 𝟐𝒚 = 𝟔.

Find the coordinates of the point where the graph cuts the y – axis.

Draw the graph of the line 𝟒𝒙 + 𝟑𝒚 = 𝟐𝟒.

(i) Write the coordinates of the points where this line intersects the x-axis and the y-axis.

(ii) Use this graph to find the area of the triangle formed by the graph line and the coordinate axes.

Draw the graphs of the lines 𝟐𝒙 + 𝒚 = 𝟔 and 𝟐𝒙 − 𝒚 + 𝟐 = 𝟎. Shade the region bounded by these lines and the x-axis. Find the area of the shaded region.

Draw the graphs of the lines 𝒙 − 𝒚 = 𝟏 and 𝟐𝒙 + 𝒚 = 𝟖. Shade the areas formed by these two lines and the y-axis. Also, find this area.

Draw the graph for each of the equations 𝒙 + 𝒚 = 𝟔 and 𝒙 − 𝒚 = 𝟐 on the same graph paper and find the coordinates of the point where the two straight lines intersect.

Two students A and B contributed ₹ 100 towards the Prime Minister’s Relief fund to help the earthquake victims. Write the linear equation to satisfy the above data and draw its graph.