Question

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

2y = 4x – 6, 2x = y + 3

Answer 1

The equations of graphs are

2y = 4x - 6

4x - 2y = 6......(i)

2x = y + 3

2x - y = 3 ....(ii)

Putting x = 0 in equation (i) we get

`=> 4 xx 0 - 2y = 6`

`=> y = -3`

`=> x = 0, y = -3`

Putting y = 0 in equation (i) we get

`=> 4x - 2xx 0 = 6`

`=> x = 3/2`

`=> x = 3/2, y = 0`

Use the following table to draw the graph.

x	0	`3/2`
y	-3	0

The graph of (i) can be obtained by plotting the two points A(0, -3), B`(3/2, 0)`

Graph of the equation (ii)

2x - y = 3 ...(ii)

Putting x = 0 in equation (ii) we get

`=> 2 xx 0 - y = 3`

`=> y = -3`

x = 0, y = -3

Putting y = 0 in equation (ii) we get

`=> 2x - 0 = 3`

`=> x = 3/2`

`x = 3/2, y = 0`

Use the following table to draw the graph.

x	0	`3/2`
y	-3	0

Draw the graph by plotting the two points C(0, -3), D`(3/2, 0)` from table.

The two lines are coincident.

Hence the equations have infinitely many solution.

Hence the system is consistent.