Question

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

2x – 3y = 6, x + y = 1

Answer 1

The given equations are

2x − 3y = 6 .....(i)

x + y = 1 .....(ii)

Putting x = 0 in equation (i) we get

`=> 2 xx 0 - 3y = 6`

`=> y = -2`

x = 0, y = -2

Putting y = 0 in equation (i) we get

`=> 2x - 3 xx 0 = 6`

`=> x = 3`

x = 3, y = 0

Use the following table to draw the graph.

x	0	3
y	-2	0

Draw the graph by plotting the two points A(0, -2), B(3, 0) from table

Graph of the equation   ...(ii)

x + y = 1   ...(ii)

Putting x = 0 in equation (ii) we get

`=> 0 + y = 1`

`=> y = 1`

:. x = 0, y = 1

Putting y = 0 in equation (ii) we get

x + 0 = 1

`=> x = 1`

x = 1, y = 0

Use the following table to draw the graph.

x	1	1
y	0	0

Draw the graph by plotting the two points C(0, 1), D(1, 0) from table.

The two lines intersect at a point `P(9/5, -4/5)`.

Hence the equations have unique solution.