Which of the following systems of inequalities has Point C as a solution? A: f(x)\leq 3x+4\\g(x)\leq -(1)/(2) x-5\\ B: f(x)\geq 3x+4\\g(x)\leq -(1)/(2) x-5 C: f(x) ≤ 3x + 4 g(x)…

Question

Which of the following systems of inequalities has Point C as a solution?

A:

`f(x)\leq 3x+4\\g(x)\leq -(1)/(2) x-5\\`

B:

`f(x)\geq 3x+4\\g(x)\leq -(1)/(2) x-5`

C:
f(x) ≤ 3x + 4

`g(x)\geq -(1)/(2)x-5`

D:
f(x) ≥ 3x + 4

`g(x)\geq -(1)/(2) x-5`

Answer 1

B

Explanation:

Answer 2

Option A.

`f(x)\leq 3x+4`

`g(x) \leq-(1)/(2)x-5`

Explanation:

we know that

If point C is a solution of the system of inequalities, then point C must satisfy both inequalities

Point C is located below the solid line f(x) and below the solid line g(x)

so

The shaded region of the solution set of the system must be below of the inequality f(x) and must be below of the inequality g(x)

therefore

The system is

`f(x)\leq 3x+4`

`g(x) \leq-(1)/(2)x-5`