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.
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 $y=0$
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