Answer
The system has infinitely many solutions, represented by-
$(x, \frac{1}{5} x +8)$
where $x$ is any real number.
Work Step by Step
Given system is-
$-\frac{1}{10}x +\frac{1}{2}y$ = $4$ __ eq.1
$2x -10y$ = $-80$ __ eq.2
Multiplying eq.1 by (-20)
$2x -10y$ = $-80$ __ eq.3
We see that both the equations in the system represent the same line. The coordinates of any point on this line give a solution of the system. Thus the system has infinitely many solutions.
Writing the equation in slope-intercept form, we have-
$10y$ = $2 x +80$
i.e. $y = \frac{2}{10} x + \frac{80}{10} $
i.e. $y = \frac{1}{5} x +8 $
i.e. for every real value of $x$,
$y = \frac{1}{5} x +8 $
Thus $(x, \frac{1}{5} x +8)$ represent the solutions of given system.
