Question 75569
Lets just plug in the possible solutions to see if they are valid. 

{{{x + 4y = 1}}} plug in (-11,3)
{{{-11 + 4(3) = 1}}}
{{{-11 + 12 = 1}}}
{{{1 = 1}}} since its true, (-11,3) is a solution



{{{x + 4y = 1}}} plug in (1,0)
{{{1 + 4(0) = 1}}}
{{{1 + 0 = 1}}}
{{{1 = 1}}} since its true, (1,0) is a solution



{{{x + 4y = 1}}} plug in (-7,-2)
{{{-7 + 4(-2) = 1}}}
{{{-7 - 8 = 1}}}
{{{-15 = 1}}} since its not true, (-7,-2) is not a solution


{{{x + 4y = 1}}} plug in (-19,5)
{{{-19 + 4(5) = 1}}}
{{{-19 + 20 = 1}}}
{{{1 = 1}}} since its true, (-19,5) is a solution

So the only solutions are (–11, 3), (1, 0), and (–19, 5)