#### Question

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

3*x** *− 5*y* = 20

6*x* − 10*y* = −40

#### Solution

The given equations are

3x - 5y = 20 ...(i)

6x - 10y = -4 ...(ii)

Putting x = 0 in equation (i) we get

`=> 3 xx 0 - 5y = 20`

=> y = -4

x= 0, y = -4

Putting y = 0 in equation (i) we get

`=> 3x - 5 xx 0 = 20`

`=> x = 20/3`

x= 20/3, y = 0

Use the following table to draw the graph.

x | 0 | 20/3 |

y | -4 | 0 |

Draw the graph by plotting the two points A(0,-4), B(20/3, 0) from table

Graph of the equation ...(ii)

6x - 10y = -4 ....(ii)

Putting x = 0 in equaion (ii) we get

`=> 6 xx 0 - 10y = -4`

`=> y = 2/5`

x = 2/5, y = 0

Putting y = 0 in equation (ii) we get

`=> 6x - 10 xx 0 = -4`

`=> x = -2/3`

x = -2/3, y = 0

Use the following table to draw the graph.

x | 0 | -2/3 |

y | 2/5 | 0 |

Draw the graph by plotting the two points C(0, -4), D(20/3, 0) from table.

Here we see that the two lines are parallel

Hence the given system of equations has no solution.