#### Question

Solve the following system of linear equations graphically and shade the region between the two lines and x-axis:

3*x* + 2*y* − 11 = 0

2*x* − 3*y** *+ 10 = 0

#### Solution

The given equations are:

3*x* + 2*y* − 11 = 0 ....(i)

2*x* − 3*y** *+ 10 = 0 ....(ii)

Putting x = 0 in equation (i) we get

`=> 3 xx 0 + 2y = 11`

`=> y = 11/2`

x = 0, y = 11/2

Putting y = 0 in eqaution (i) we get

`=> 3x + 2 xx 0 = 11`

=> x = 11/3

x = 11/3, y = 0

Use the following table to draw the graph.

x | 0 | 11/3 |

y | 11/2 | 0 |

Draw the graph by plotting the two points A(0,11/2), B(11/3, 0) from table

2x - 3y + 10 = 0 ....(ii)

Putting x = 0 in equation (ii) we get

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

=> y = 10/3

x = 0, y = 10/3

Putting y = 0 in equation (ii) 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), D(-5,0) from table.

The two lines intersect at P(1,4). The area enclosed by the lines represented by the given equations and the coordinates x−axis and shaded the area in the graph.

Hence, x = 1 and y = 4 and is the solution.