#### Question

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

3*x* − 4*y* − 1 = 0

`2x - 8/3y + 5 = 0`

#### Solution

The given equations are

3x - 4y - 1 = 0 .....(i)

`2x - 8/3 y + 5 = 0`

6x - 8y + 15 = 0 ...(ii)

Putting x = 0 in equation (i) we get

` => 3 xx 0 - 4y = 1`

`=>` y = -1/4

=> x = 0, y = -1/4

Putting y = 0 in equation (i) we get

`=> 3x - 4xx0 = 1`

=> x = 1/2

=> x = 1/3, y = 0

Use the following table to draw the graph.

x | 0 | 1/3 |

y | -1/4 | 0 |

The graph of (*i*) can be obtained by plotting the two points A(0, -1/4), B(1/3, 0)

6x - 8y = -15 ....(ii)

Putting x = 0 in equation (ii) we get

`=> 6 xx 0 - 8y = -15`

`=> y = 15/8`

=> x = 0, y = 15/8

Putting y = 0 in equation (ii) we get

`=> 6x - 8 xx 0 = -15`

=> x = -15/6

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

Use the following table to draw the graph.

x | 0 | -5/2 |

y | 15/8 | 0 |

Draw the graph by plotting the two point C(0,15/8), D(-5/2, 0) from table

Here, the two lines are parallel.

Hence the given system of equations is inconsistent.