Question

Is (0,0) a solution to this system? y ≥ x^2 - 4 y < 2x - 1

A. Yes. (0,0) satisfies both inequalities.

B. No. (0,0) satisfies y < 2x - 1 but does not satisfy y ≥ x^2 - 4.

C. No. (0,0) does not satisfy either inequality.

D. No. (0,0) satisfies y ≥ x^2 - 4 but does not satisfy y < 2x - 1.

Answer 1

The answer is C
If we replace the variables with 0 the equation looks like this
0 >/ 0^2-4 and there isn't a possible answer if you put it in the calculator
and 0<2(0)-1= 0< (-1) and in mathematics a negative number is a real number that is less than zero. I hope this helps please tell me if I'm wrong.

Answer 2

The inequality y ≥ x^2-4 satisfies (0,0) but the inequality y < 2x-1

does not satisfy (0,0).  

Finding solution of both the inequalities:

• Consider the inequality  y ≥ x^2-4   -------(i)

          Substitute (x,y)=  (0,0) in the above inequality

                                   0 ≥ (0^2)-4

                                         0 ≥ -4

              The above inequality is true.

             Hence, (0,0) is the solution of inequality (i)

• Consider the inequality y < 2x-1   ---------(ii)

          Substitute (x,y)=  (0,0) in the above inequality

                                0 < 2(0) - 1

                                0 <  -1

                The above inequality is not true.

          Hence (0,0) does not satisfy the above inequality (ii).

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