Solve the following system of linear equations graphically.

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$$.(i) 3 x+5 y-15=0(ii) Putting x=0 in equation (i), we get: \Rightarrow 4 \times 0-5 y=20 \Rightarrow y=-4 x=0, \quad y-4 Putting y=0 in equation (i) we get: \Rightarrow 4 x-5 \times 0=20 \Rightarrow x=5 x=5, \quad y=0 Use the following table to draw the graph. Draw the graph by plotting the two points from table 3 x+5 y=15$$\ldots(i i)$

Putting $x=0$ in equation (ii) we get:

$\Rightarrow 3 \times 0+5 y=15$

$\Rightarrow y=3$

$x=0, \quad y=3$

Putting $y=0$ in equation (ii) we get:

$\Rightarrow 3 x+5 \times 0=15$

$\Rightarrow x=5$

$x=5, \quad y=0$

Use the following table to draw the graph.

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 $y=0$