The path of a train A is given by the equation 3x + 4y − 12 = 0 and the path of another train B is given by the equation 6x + 8y − 48 = 0. Represent this situation graphically.
The given equation are $3 x+4 y-12=0$ and $6 x+8 y-48=0$.
In order to represent the above pair of linear equation graphically, we need
Two points on the line representing each equation. That is, we find two solutions
of each equation as given below:
We have,
$3 x+4 y-12=0$
Putting $y=0$, we get
$3 x+0-12=0$
$\Rightarrow x=4$
Putting $x=0$ we get
$0+4 y-12=0$
$\Rightarrow y=3$
Thus, two solution of equation $3 x+4 y-12=0$ are
We have $6 x+8 y-48=0$
Putting $y=0$, we get
$6 x+0-48=0$
$\Rightarrow x=8$
Putting $x=0$ we get
$0+8 y-48=0$
$\Rightarrow y=6$
Thus, two solution of equation $6 x+8 y-48=0$ are
Now we plot the point $A(4,0)$ and $B(0,3)$ and draw a line passing through
These two points to get the graph o the line represented by equation(1)
We also plot the points $C(8,0)$ and $D(0,6)$ and draw a line passing through
These two points to get the graph $\mathrm{O}$ the line represented by equation $(2)$
We observe that the line parallel and they do not intersect anywhere.
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