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 $y\geqslant \frac {1}{5}x-4$ and $y\gt -x-3$, we need to substitute into the inequalities and check if they satisfy both inequalities.<br /><br />Let's start with the first point $(0,-5)$:<br />Substituting $(0,-5)$ into the first inequality $y\geqslant \frac {1}{5}x-4$, we get:<br />$-5\geqslant \frac {1}{5}(0)-4$<br />$-5\geqslant -4$<br />This is not true, so $(0,-5)$ is not a solution.<br /><br />Now let's substitute $(0,-5)$ into the second inequality $y\gt -x-3$:<br />$-5\gt -(0)-3$<br />$-5\gt -3$<br />This is also not true, so $(5)$ is not a solution.<br /><br />Next, let's substitute $(-5,0)$ into the inequalities:<br />Substituting $(-5,0)$ into the first inequality $y\geqslant \frac {1}{5}x-4$, we get:<br />$0\geqslant \frac {1}{5}(-5)-4$<br />$0\geqslant -1-4$<br />$0\geqslant -5$<br />This is true, so $(-5,0)$ satisfies the first inequality.<br /><br />Now let's substitute $(-5,0)$ into the second inequality $y\gt -x-3$:<br />$0\gt -(-5)-3$<br />$03$<br />$0\gt 2$<br />This is not true, so $(-5,0)$ does not satisfy the second inequality.<br /><br />Moving on to the point $(0,0)$:<br />Substituting $(0,0)$ into the first inequality $y\geqslant \frac {1}{5}x-4$, we get:<br />$0\geqslant \frac {1}{5}(0)-4$<br />$0\geqslant -4$<br />This is true, so $(0,0)$ satisfies the first inequality.<br /><br />Now let's substitute $(0,0)$ into the second inequality $y\gt -x-3$:<br />$0\gt -(0)-3$<br />$0\gtThis is true, so $(0,0)$ satisfies the second inequality.<br /><br />Finally, let's substitute $(5,0)$ into the inequalities:<br />Substituting $(5,0)$ into the first inequality $y\geqslant \frac {1}{5}x-4$, we get:<br />$0\geqslant \frac {1}{5}(5)-4$<br />$0\geqslant 1-4$<br />$0\geqslant -3$<br />This is true, so $(5,0)$ satisfies the first inequality.<br /><br />Now let's substitute $(5,0)$ into the second inequality $y\gt-3$:<br />$0\gt -(5)-3$<br />$0\gt -8$<br />This is true, so $(5,0)$ satisfies the second inequality.<br /><br />Therefore, the point $(5,0)$ is a solution to the system of inequalities $y\geqslant \frac {1}{5}x-4$ and $y\gt -x-3$.