Which of the following points is a solution to the system of inequalities ygeqslant (1)/(5)x-4 and ygt -x-3 (0,-5) (-5,0) (0,0) (5,0)

To determine which of the given points is a solution to the system of inequalities and , we need to substitute into the inequalities and check if they satisfy both inequalities.Let's start with the first point :Substituting into the first inequality , we get: This is not true, so is not a solution.Now let's substitute into the second inequality : This is also not true, so is not a solution.Next, let's substitute into the inequalities:Substituting into the first inequality , we get: This is true, so satisfies the first inequality.Now let's substitute into the second inequality : This is not true, so does not satisfy the second inequality.Moving on to the point :Substituting into the first inequality , we get: This is true, so satisfies the first inequality.Now let's substitute into the second inequality : (0,0) (5,0) (5,0) y\geqslant \frac {1}{5}x-4 0\geqslant \frac {1}{5}(5)-4 0\geqslant 1-4 0\geqslant -3 (5,0) (5,0) y\gt-3 0\gt -(5)-3 0\gt -8 (5,0) (5,0) y\geqslant \frac {1}{5}x-4 y\gt -x-3$.