Answer:
All points satisfy the inequality
Step-by-step explanation:
Given
[tex]5x + 2y \le 26[/tex]
Required
Select all points that satisfy the above inequality
[tex](a)\ (0,5)[/tex]
This implies that
[tex]x = 0; y = 5[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 0 + 2 * 5 \le 26[/tex]
[tex]0 + 10 \le 26[/tex]
[tex]10 \le 26[/tex]
This satisfy the inequality
[tex](b)\ (3,1)[/tex]
This implies that
[tex]x = 3;\ y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * 1 \le 26[/tex]
[tex]15 + 2 \le 26[/tex]
[tex]17 \le 26[/tex]
This satisfy the inequality
[tex](c)\ (3,-4)[/tex]
This implies that:
[tex]x = 3; y-4[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * -4 \le 26[/tex]
[tex]15 -8 \le 26[/tex]
[tex]7 \le 26[/tex]
This satisfy the inequality
[tex](d)\ (-4,1)[/tex]
This implies that:
[tex]x = -4; y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * -4 + 2 *1 \le 26[/tex]
[tex]-20 + 2 \le 26[/tex]
[tex]-18 \le 26[/tex]
This satisfy the inequality
