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