#### Question

Solve the following systems of equations graphically:

x − 2y = 5

2*x* + 5*y* = 12

#### Solution

The given equations are:

x + y = 3 ....(1)

2x + 5y = 12 ....(2)

Putting x = 0 in equation 1 we get:

`=> 0 + y = 3`

=> y = 3

x = 0, y = 3

Putting y = 0 in equation 1 we get

=> x + 0 = 3

=> x = 3

x = 3 , y = 0

Use the following table to draw the graph.

x | 0 | 3 |

y | 3 | 0 |

Draw the graph by plotting the two points A(0,3) and B(3,0) from table

Graph of the equation (2)

=> 2x + 5y = 12

Putting x = 0 in equation (2), we get

`=> 2 xx 0 + 5y = 12``

=> 5y = 12

`=> y = 12/5`

x = 0, y = 12/5

Putting y = 0 in equation (2) we get

`=> 2x + 5 xx 0 = 12`

`=> 2x = 12`

`=> x = 6`

`x = 6, y = 0`

Use the following table to draw the graph.

x | 0 | 6 |

y | 12/5 | 0 |

Draw the graph by plotting the two points C(0, 12/5), D(6,0) from the table.

The two line intersect at point P(1,2)

Hence x = 1 and y = 2 is the solution