#### Question

Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution) :

2*y* − *x* = 9

6*y* − 3*x* = 21

#### Solution

The given equations are

2y - x = 9 ...(i)

6y - 3x = 21 ....(ii)

Putting x = 0 in equation (i) we get

`=> 2y - 0 = 9`

`=> y = 9/2`

x = 0, y = 9/2

Putting y= 0 in equation (i) weget

`=> 2 xx -x = 9`

`=> x = -9`

`=> x = -9, y = 0`

Use the following table to draw the graph.

x | 0 | -9 |

y | 9/2 | 0 |

Draw the graph by plotting the two points A(0, 9/2), B(-9,0) from table

6y - 3x = 21 ...(ii)

Putting x = 0 in equation (ii) we get

`=> 6y - 3 xx 0 = 21`

`=> y = 7/2`

=> x = 0, y = 7/2

Putting y = 0 in equation (ii) we get

`=> 6 xx 0 - 3x = 21`

=> x = -7

`:. x = -7, y= 0`

Use the following table to draw the graph.

x | 0 | -7 |

y | 7/2 | 0 |

Draw the graph by plotting the two points C(0, 7/2), D(-7,0) from table.

Here two lines are parallel and so don’t have common points

Hence the given system of equations has no solution.