y \geq \frac{3}{10}x+5 \newline y > 5x-7 $\newline$ Which of the following ordered pairs $(x,y)$ satisfies the system of inequalities? $\newline$ Choose $1$ answer: $\newline$ (A) $(0,5)$ $\newline$ (B) $(1,1)$ $\newline$ (C) $(3,8)$ $\newline$ (D) $(10,6)$

Full solution

y \geq \frac{3}{10}x+5 \newline y > 5x-7

\newline

Which of the following ordered pairs

(x,y)

satisfies the system of inequalities?

\newline

Choose

1

answer:

\newline

(A)

(0,5)

\newline

(B)

(1,1)

\newline

(C)

(3,8)

\newline

(D)

(10,6)

Step $1$ : Check first inequality: Check if the ordered pair $(0,5)$ satisfies both inequalities. $\newline$ First inequality: $y \geq \frac{3}{10}x + 5$ $\newline$ Substitute $x = 0$ and $y = 5$ into the inequality. $\newline$ $5 \geq \frac{3}{10}\cdot0 + 5$ $\newline$ $5 \geq 5$ $\newline$ This is true.
Step $2$ : Check second inequality: Check the second inequality for the ordered pair $(0,5)$ . $\newline$ Second inequality: y > 5x - 7 $\newline$ Substitute $x = 0$ and $y = 5$ into the inequality. $\newline$ 5 > 5\cdot0 - 7 $\newline$ 5 > -7 $\newline$ This is also true.
Step $3$ : Confirm solution: Since the ordered pair $(0,5)$ satisfies both inequalities, we have found a solution. We do not need to check the other options as the question asks for only one correct answer.