Question

Solve the following systems of equations graphically:
x − 2y = 6

3x − 6y = 0

Answer 1

The given equations are:

x − 2y = 6   ...(i)

3x − 6y = 0 ...(ii)

Putting x = 0 in equation (i) we get

=> 0 - 2y = 6

=> y = -3

x = 0,  y = -3

Putting y = 0 in equation (i) we get

`=> x - 2 xx 0 = 6`

`=> x = 6`

x = 6, y = 0

Use the following table to draw the graph

x	0	6
y	-3	0

Plotting the two points A(0, -3) and B(6,0) equaion (1) can be drawn

Graph of the equation ..(ii)

3x - 6y = 0 ...(ii)

Putting x = 0 in equation (ii) we get

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

=> y = 0

x = 0, y = 0

Putting x = 2 in equation (2) we get

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

=> y = 1

x = 2, y = 1

Use the following table to draw the graph.

x	0	2
y	0	1

Draw the graph by plotting the two points O(0,0) and D(2,1) from table

We see that the two lines are parallel, so they won’t intersect

Hence there is no solution