Check graphically whether the pair of linear equation 4x − y − 8 = 0 and 2x − 3y + 6 = 0 is consistent. Also, find the vertices of the triangle formed by these lines with the x-axis.
Here we have to draw the graph between two equations given by
$4 x-y-8=0$.........(1)
$2 x-3 y+6=0$............(2)
Also we have to find the vertices of the triangle form by the x-axis and these lines.
The first equation can written as follow
$y=4 x-8$ ............(3)
Now we are going to find the value of y at different value of x
Now mark the points (0,-8) and (2, 0) on xy −plane and we will draw a line which passes through these two points.
The second equation can be written as
$y=\frac{2 x+6}{3}$.............(4)
Now mark the points (0, 2) and (3, 4) on xy −plane and we will draw a line which passes through these two points.
From the above analysis, we have the following graph
From the above graph the vertices A, B and C are given as follow.
$A=(3,4)$
$B=(2,0)$
$C=(-3,0)$
Hence the vertices are $(3,4),(2,0)(-3,0)$
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