Question

Find the number of solutions which are common to both $y=8x+3\&5y-x=1,$ if any.

Answer 1

Let's rewrite the equation of lines in slope form $y=mx+c.$
$y=8x+3$
Here, slope, $m=8$

and, $5y=x+1,$
$\Rightarrow y=\frac{1}{5}x+\frac{1}{5}$
Here, slope, $m=\frac{1}{5}$

As slope of both the lines are different, they will meet at a point.
Hence, there is one solution which is common to both given equation.