Given system of equations are:
$x–2y–8=0$
$5x–10y–10=0$
Above equations are of the form
${{a}_{1}}x+{{b}_{1}}y-{{c}_{1}}=0$
${{a}_{2}}x+{{b}_{2}}y-{{c}_{2}}=0$
Here,${{a}_{1}}=1.{{b}_{1}}=-2,{{c}_{1}}=-8$
${{a}_{2}}=5,{{b}_{2}}=-10,{{c}_{2}}=-10$
According to the question, we get
${{a}_{1}}/{{a}_{2}}=1/5$
${{b}_{1}}/{{b}_{2}}=-2/-10=1/5$
${{c}_{1}}/{{c}_{2}}=-8/-10=4/5$
$\Rightarrow {{a}_{1}}/{{a}_{2}}={{b}_{1}}/{{b}_{2}}\ne {{c}_{1}}/{{c}_{2}}$
Thus, we can conclude that the given equation has no solution