#### Question

Solve the following systems of equations graphically:

x − 2y = 5

2x + 3y = 10

#### Solution

The given equations are

x - 2y = 5 ...(1)

2x + 3y = 10 ...(2)

Putting x = 0 in equation (1) we get

`=> 0 - 2y = 5`

=> y = -5/2

x = 0, y = -5/2

Putting y = 0 in equation (1) we get

`=> x + 2 xx 0 = 5`

`=> x = 5`

x = 5, y = 0

Use the following table to draw the graph.

x | 0 | 5 |

y | -5/2 | 0 |

Draw the graph by plotting the two points A(0, -5/2) and B(5,0) from table

Graph the equation (2)

`=>2x + 3y = 10 ...(2)`

Putting x = 0 i equation (ii) we get

`=> 2 xx 0 + 3y =10`

`=> y = 10/3`

x = 0, y = 10/3

Putting y = 0 in equation (2) we get

`=>2x + 3 xx 0 = 10`

=> x = 5

x = 5, y = 0

Use the following table to draw the graph.

x | 0 | 5 |

y | 10/3 | 0 |

Draw the graph by plotting the two points C(0,10/3) and B(5,0) from table

The two lines intersects at point B(5,0)

Hence x = 5, y = 0 is the solution