Question

Is (0,0) a solution to this system?

y ²x²-4
y< 2x-1
A. No. (0,0) satisfies y 42-4 but does not satisfy y< 2x-1.
B. No. (0,0) does not satisfy either inequality.
C. No. (0,0) satisfies y< 2x- 1 but does not satisfy yz 22.4.
O D. Yes. (0,0) satisfies both inequalities.

Answer 1

A. Solution to
`y \ge x^2 - 4` but not to
`y < 2x - 1`

Explanation:

Given

`y \ge x^2 - 4`

`y < 2x - 1`

Required

Is
`(0,0)` a solution?

`(0,0)` implies that:

`x = 0\ and\ y = 0`

To check if it is a solution or not, we simply substitute 0 for x and for y in the given inequalities

`y \ge x^2 - 4` becomes

`0 \ge 0^2 - 4`

`0 \ge 0- 4`

`0 \ge - 4`

This solution is true

`y < 2x - 1` becomes

`0 < 2 * 0 - 1`

`0 < 0 - 1`

`0 < - 1`

This solution is not true because 0 is greater than 1.

Hence, option (A) is correct