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

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

(i) ?? + ?? = ?. ?

(ii) ?? −?/?+ ? = ?

(iii) ?? − ?? = ?

(iv) ?? = ??

(v)?/?−?/?= ?

(vi) √?? + √?? = ?

Express each of the following equations in the form ?? + ?? + ? = ? and indicate the values of a, b,

c in each case.

(i) ? = ?

(ii) ?? − ? = ? − ?

(iii) ?? + ? = ?

(iv) ?? = ?

(v) ? + ? = ?

(vi)?/?−?/?=?/?+ ?

Check which of the following are the solutions of the equation ?? − ?? = ??.

(i) (4, 0)

(ii) (0, 5)

(iii) (-2, ?/?)

(iv) (0, -5)

(v) (2, − ?/?)

Find five different solutions of each of the following equations.

(a) ?? − ?? = ?

(b) ??/?+??/??= ?

(c) ?? = ??

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

If ? = ?? + ? and ? = ?? − ? is a solution of the equation ?? − ?? + ? = ?, 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).

Draw the graph of each of the following equations.

(i) ? = ?

(ii) ? + ? = ?

(iii) ? = ?

(iv) ? = −?

(v) ? = −?

(vi) ? = ?

(vii) ? + ? = ?

(viii) ? = ?

Draw the graph of the equation ? = ??.

From your graph, find the value of y when

(i) ? = ?

(ii) ? = −?

Draw the graph of the equation ? + ?? − ? = ?.

From your graph, find the value of y when

(i) ? = ?

(ii) ? = −?

Draw the graph of the equation, ?? − ?? = ?.

From your graph, find

(i) The value of y when ? = ?

(ii) The value of x when ? = ?.

Draw the graph of the equation, ?? + ? = ?.

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

Draw the graph of the equation, ?? + ?? = ?.

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

Draw the graph of the line ?? + ?? = ??.

(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 ?? + ? = ? and ?? − ? + ? = ?. Shade the region bounded by these lines and the x-axis. Find the area of the shaded region.

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

Draw the graph for each of the equations ? + ? = ? and ? − ? = ? 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.