The answers are (0,0) and (-2,-3). The explanation is below and let me know if you need any clarifications, thanks!
Point (5,1):
Let's test this point for the first inequality of the system
[tex]y \leq \dfrac{1}{5}x[/tex]
[tex]1\leq \dfrac{1}{5} \times 5[/tex]
[tex]1\leq 1[/tex]
1 is equal to 1; thus this point works for the first inequality. Now, let's test the point for the second inequality of the system
[tex]y>4x-3[/tex]
[tex]1>4(5)-3[/tex]
[tex]1>17[/tex]
Since 1 is NOT greater than 17, this point does not satisfy the second inequality. Thus, point (5,1) is not a solution
Point (0,0):
Let's test this point for the first inequality of the system
[tex]y \leq \dfrac{1}{5}x[/tex]
[tex]0\leq \dfrac{1}{5} \times 0[/tex]
[tex]0\leq 0[/tex]
0 is equal to 0; thus this point works for the first inequality. Now, let's test the point for the second inequality of the system
[tex]y>4x-3[/tex]
[tex]0>4(0)-3[/tex]
[tex]0>-3[/tex]
0 is greater than -3. This point satisfies both inequalities, making it a solution to the system.
Point (-2,-3):
Let's test this point for the first inequality of the system
[tex]y \leq \dfrac{1}{5}x[/tex]
[tex]-3\leq \dfrac{1}{5} \times (-2)[/tex]
[tex]-3\leq -\dfrac{2}{5}[/tex]
This inequality is true; thus, this point satisfies the first inequality. Now, let's test the point for the second inequality of the system
[tex]y>4x-3[/tex]
[tex]-3>4(-2)-3[/tex]
[tex]-3>-11[/tex]
-3 is greater than -11. This point satisfies both inequalities, making it a solution to the system.
Point (2,5):
Let's test this point for the first inequality of the system
[tex]y\leq \dfrac{1}{5}x[/tex]
[tex]5\leq \dfrac{2}{5}[/tex]
This inequality is NOT true. Since this point does not satisfy the first inequality, it cannot be a solution to the system.
~ Padoru
