Question

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.

Answer 1

Answer: 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.

Answer 2

option-B

Explanation:

we are given system of inequality as

`y\leq x^2-4`

`y>2x-1`

now, we can check solution

At (0,0):

we can plug x=0 and y=0

and check inequality

`0\leq 0^2-4`

`0\leq -4`

so, this is FALSE

now, we can check second inequality

`0>2* 0-1`

`0>-1`

So, this is TRUE

so, option-B