#### Question

Solve the following system of linear equations graphically

4*x* − 5*y* − 20 = 0

3*x* + 5*y* − 15 = 0

Determine the vertices of the triangle formed by the lines representing the above equation and the *y*-axis.

#### Solution

The given equations are:

4*x* − 5*y* − 20 = 0 ........(i)

3*x* + 5*y* − 15 = 0 ..........(ii)

Putting x = 0 in equation (i) we get:

`=> 4 xx 0 - 5y = 20`

`=> y = -4`

x = 0, y - 4

Putting y = 0 in eqaution (i) we get

`=> 4x - 5 xx 0 = 20`

=> x = 5

x = 5, y = 0

Use the following table to draw the graph.

x | 0 | 5 |

y | -4 | 0 |

Draw the graph by plotting the two points from table

3x + 5y = 15 .....(ii)

Putting x = 0 in eqaution (ii) we get

`=> 3 xx 0 + 5y = 15`

=> x = 5

x = 5, y = 0

Use the following table to draw the graph.

x | 0 | 5 |

y | 3 | 0 |

Draw the graph by plotting the two points from table.

The three vertices of the triangle are A(0, -4), B(5,0), and C(0,3)

Hence the solution of the equation is x = 5 and y = 0