Show graphically that each one of the following systems of equations has infinitely many solutions:
$3 x+y=8$
$6 x+2 y=16$
The given equations are
$3 x+y=8$...(i)
$6 x+2 y=16$...(ii)
Putting $x=0$ in equation $(i)$, we get:
$\Rightarrow 3 \times 0+y=8$
$\Rightarrow y=8$
$x=0, \quad y=8$
Putting $y=0$ in equations $(i)$ we get:
$\Rightarrow 3 x+0=8$
$\Rightarrow x=8 / 3$
$x=8 / 3, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $A(0,8)$ and $B(8 / 3,0)$ from table.
Graph of the equation….
$6 x+2 y=16$ ...(ii)
Putting $x=0$ in equations $(i i)$ we get:
$\Rightarrow 6 \times 0+2 y=16$
$\Rightarrow y=8$
$x=0, \quad y=8$
Putting $y=0$ in equation $(i i)$, we get:
$\Rightarrow 6 x+2 \times 0=16$
$\Rightarrow x=8 / 3$
$x=8 / 3, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $C(0,8), D(8 / 3,0)$ from table.
Thus the graph of the two equations coincide
Consequently, every solution of one equation is a solution of the other.
Hence the equations have infinitely many solutions.
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