Is (0,0) a solution to this system? y ≤ x^2 - 4 y > 2x - 1 a. no. (0,0) satisfies y ≤ x^2- 4 but does not satisfy y > 2x - 1. b. no. (0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. c. yes. (0,0) satisfies both inequalities. d. no. (0,0) does not satisfy either inequality.

Hello mate!

we want to know if the pair (0,0) is a solution for the system, where the usual notation for a pair is (x,y), and the system is:

y ≤ x^2 - 4

y > 2x - 1

The first step is replacing the numbers in the system by the numbers in the pair, and look if the pair is a solution or not.

the first inequality gets:

y ≤ x^2 - 4

0 ≤ 0^2 - 4

0 ≤ - 4

This is false, so (0,0) is not a solution for this inequality.

Now let's see the second one:

y > 2x - 1

0 > 2*0 - 1

0 > -1

This is true, then the pair (0,0) is a solution for this inequality.

then the answer is the option B, the pair (0,0) is not a solution for the system, satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4.

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