#### Question

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

#### Solution

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 = 0in 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