Question

Determine, by drawing graphs, whether the following system of linear equations has a unique solution or not :

(i) 2x − 3y = 6, x + y = 1
(ii) 2y = 4x − 6, 2x = y + 3

Answer 1

(i) 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.

Graph of the equation….

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 point .

Hence the equations have unique solution.

(ii) The equations of graphs is

Putting in equation we get:

Putting in equation we get:

Use the following table to draw the graph.

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

Graph of the equation

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.

The two lines are coincident.

Hence the equations have infinitely much solution.

Hence the system is consistent