Question

Solve the following system of linear equation graphically and shade the region between the two lines and x-axis:

(i) 2x + 3y = 12,
x − y = 1

(ii) 3x + 2y − 4 = 0,
2x − 3y − 7 = 0

(iii) 3x + 2y − 11 = 0
2x − 3y + 10 = 0

Answer 1

The given equations are:

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

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. The region enclosed by the lines represented by the given equations and x−axis are shown in the above figure

Hence, and is the solution.

(ii) The given equations are:

Putting in equation we get:

Putting in equationwe get:

Use the following table to draw the graph.

	0
	2	0

The graph of (i) can be obtained by plotting the two points.

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. The area enclosed by the lines represented by the given equations and the coordinates x−axis and shaded the area in graph.

Hence, and is the solution.

(iii) The given equations are:

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

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. The area enclosed by the lines represented by the given equations and the coordinates x−axis and shaded the area in graph.

Hence, and is the solution.