Question

which of the following is a solution to this system of equations:
\

$$\begin{cases} 3x - 4y \\geq -1 \\\\ y \\geq -4 \\end{cases}$$

\bigcirc \\ (0, 2)
\bigcirc \\ (-1, -5)
\bigcirc \\ (-2, -1)
\bigcirc \\ (2, 1)

Explanation:

Step1: Check (0,2)

First inequality: $3(0)-4(2)=-8 \geq -1$? No. Wait correction: $3(0)-4(2)=-8$, which is less than -1, so (0,2) fails first inequality.
Second inequality: $2 \geq -4$ yes, but first fails.

Step2: Check (-1,-5)

Second inequality: $-5 \geq -4$? No, so fails.

Step3: Check (-2,-1)

First inequality: $3(-2)-4(-1)=-6+4=-2 \geq -1$? No correction: $3(-2)-4(-1)=-6+4=-2 < -1$, fails first. Wait correction again: $3(-2)-4(-1)= -6 +4 = -2$, which is less than -1, no. Wait (2,1): $3(2)-4(1)=6-4=2 \geq -1$ yes; $1 \geq -4$ yes. (-2,-1): $3(-2)-4(-1)= -6+4=-2 < -1$ no. (0,2): $3*0 -4*2=-8 < -1$ no. (-1,-5): y=-5 < -4 no. So only (2,1) works.

Step1: Verify (-1,-5)

$y=-5 < -4$ → fails second inequality.

Step2: Verify (0,2)

$3(0)-4(2)=-8 < -1$ → fails first inequality.

Step3: Verify (-2,-1)

$3(-2)-4(-1)=-2 < -1$ → fails first inequality.

Step4: Verify (2,1)

$3(2)-4(1)=2 ≥ -1$ and $1 ≥ -4$ → both hold.

Final Answer: (2,1)

Answer:

(0, 2), (-2, -1), (2, 1)