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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.

Is 00 a solution to this system y x4 ylt 2x1 A No 00 satisfies y 424 but does not satisfy ylt 2x1 B No 00 does not satisfy either inequality C No 00 satisfies y class=

Respuesta :

MrRoyal

Answer:

A. Solution to [tex]y \ge x^2 - 4[/tex] but not to [tex]y < 2x - 1[/tex]

Step-by-step explanation:

Given

[tex]y \ge x^2 - 4[/tex]

[tex]y < 2x - 1[/tex]

Required

Is [tex](0,0)[/tex] a solution?

[tex](0,0)[/tex] implies that:

[tex]x = 0\ and\ y = 0[/tex]

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

[tex]y \ge x^2 - 4[/tex] becomes

[tex]0 \ge 0^2 - 4[/tex]

[tex]0 \ge 0- 4[/tex]

[tex]0 \ge - 4[/tex]

This solution is true

[tex]y < 2x - 1[/tex] becomes

[tex]0 < 2 * 0 - 1[/tex]

[tex]0 < 0 - 1[/tex]

[tex]0 < - 1[/tex]

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

Hence, option (A) is correct

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