Question

Solve the following system of linear equations graphically :

3x + y − 11 = 0, x − y − 1 = 0.
Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.

Answer 1

The given equations are

Putting in equation we get:

Putting in equation we get:

Use the following table to draw the graph.

Draw the graph by plotting the two points from table.

Putting in equation we get:

Putting in equationwe get:

Use the following table to draw the graph.

Draw the graph by plotting the two points from table.

The two lines intersect at.

Hence is the solution of the given equations

The area enclosed by the lines represented by the given equations and the y−axis is shaded region in the figure

Now, Required area = Area of shaded region

Required area = Area of PAC

Required area =

Required area =

Required area =

Hence the required area is sq. unit