Question

Which point represents a solution to the system y<=1/5x, y>4x-3? Select all that apply. (5, 1) (0, 0) (-2, -3) (2, 5)

Answer 1

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

`y \leq (1)/(5)x`

`1\leq (1)/(5) * 5`

`1\leq 1`

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

`y>4x-3`

`1>4(5)-3`

`1>17`

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

`y \leq (1)/(5)x`

`0\leq (1)/(5) * 0`

`0\leq 0`

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

`y>4x-3`

`0>4(0)-3`

`0>-3`

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

`y \leq (1)/(5)x`

`-3\leq (1)/(5) * (-2)`

`-3\leq -(2)/(5)`

This inequality is true; thus, this point satisfies the first inequality. Now, let's test the point for the second inequality of the system

`y>4x-3`

`-3>4(-2)-3`

`-3>-11`

-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

`y\leq (1)/(5)x`

`5\leq (2)/(5)`

This inequality is NOT true. Since this point does not satisfy the first inequality, it cannot be a solution to the system.

~ Padoru