Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :
Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution) :
$x-2 y=6$
$3 x-6 y=0$
The given equations are
$x-2 y=6$$.(i)$
$3 x-6 y=0$..(ii)
Putting $x=0$ in equation $(i)$, we get:
$\Rightarrow 0-2 y=6$
$\Rightarrow y=-3$
$\Rightarrow x=0, \quad y=-3$
Putting $y=0$ in equation $(i)$ we get:
$\Rightarrow x-2 \times 0=6$
$\Rightarrow x=6$
$\Rightarrow x=6, \quad y=0$
Use the following table to draw the graph.
The graph of $(i)$ can be obtained by plotting the two points $A(0,-3), B(6,0)$.
Graph of the equation.... (ii):
$3 x-6 y=0$ .. (ii)
Putting $x=0$ in equation (ii) we get:
$\Rightarrow 3 \times 0-6 y=0$
$\Rightarrow y=0$
$\Rightarrow x=0, \quad y=0$
Putting $y=1$ in equation $(i i)$, we get:
$\Rightarrow 3 x-6 \times 1=0$
$\Rightarrow x=2$
$\Rightarrow x=2, \quad y=1$
Use the following table to draw the graph.
Draw the graph by plotting the two points $C(0,0), D(2,1)$ from table.
Here the two lines are parallel and so there is no point in common
Hence the given system of equations has no solution.
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