Question

Which of the following points satisfies the linear inequality below? Select all correct answers.

5x + 2y 26
Select all that apply:
(0,5)
(3,1)
(3,-4)
(-4,1)

Answer 1

All points satisfy the inequality

Explanation:

Given

`5x + 2y \le 26`

Required

Select all points that satisfy the above inequality

`(a)\ (0,5)`

This implies that

`x = 0; y = 5`

So, we have:

`5x + 2y \le 26`

`5 * 0 + 2 * 5 \le 26`

`0 + 10 \le 26`

`10 \le 26`

This satisfy the inequality

`(b)\ (3,1)`

This implies that

`x = 3;\ y =1`

So, we have:

`5x + 2y \le 26`

`5 * 3 + 2 * 1 \le 26`

`15 + 2 \le 26`

`17 \le 26`

This satisfy the inequality

`(c)\ (3,-4)`

This implies that:

`x = 3; y-4`

So, we have:

`5x + 2y \le 26`

`5 * 3 + 2 * -4 \le 26`

`15 -8 \le 26`

`7 \le 26`

This satisfy the inequality

`(d)\ (-4,1)`

This implies that:

`x = -4; y =1`

So, we have:

`5x + 2y \le 26`

`5 * -4 + 2 *1 \le 26`

`-20 + 2 \le 26`

`-18 \le 26`

This satisfy the inequality