Question

Determine, graphically whether the system of equations x – 2y = 2, 4x – 2y = 5 is consistent or in-consistent.

Determine, graphically whether the following system of linear equations is consistent or in-consistent:

x – 2y = 2, 4x – 2y = 5

Answer 1

The given equations are

x – 2y = 2 ....(i)

4x – 2y = 5  ....(ii)

Putting x = 0 in equation (i) we get

`=> 0 - 2y = 2`

`=> y = -1`

`=> x = 0, y = -1`

Putting y = 0 in equation (i) we get

`=> x - 2 xx 0 = 2`

`=> x = 2`

`=> x = 2, y = 0`

Use the following table to draw the graph.

x	0	2
y	–1	0

Draw the graph by plotting the two points A(0, –1), B(2, 0) from table.

4x – 2y = 5 .....(ii)

Putting x = 0 in equation (ii) we get

`=> 4 xx 0 - 2y = 5`

`=> y = -5/2`

`=> x = 0, y = -5/2`

Putting y = 0 in equation (ii) we get

`=> 4x - 2 xx 0 = 5`

`=> y = 5/4`

`=> x = 5/4, y = 0`

Use the following table to draw the graph

x	0	`5/4`
y	`-5/2`	0

Draw the graph by plotting the two points `C(0, -5/2), D(5/4, 0)` from the table.

It has a unique solution.

Hence the system of equations is consistent.