Question

graphs of linear systems and inequalities: medium
$y\geq\frac{3}{10}x + 5$
$y>5x - 7$
which of the following ordered pairs $(x,y)$ satisfies the system of inequalities?
choose 1 answer:
(a) $(0,5)$
(b) $(1,1)$
(c) $(3,8)$
(d) $(10,6)$

Explanation:

Step1: Test option A (0, 5)

For $y\geq\frac{3}{10}x + 5$, substitute $x = 0$ and $y=5$: $5\geq\frac{3}{10}\times0 + 5$, which is $5\geq5$ (true).
For $y>5x - 7$, substitute $x = 0$ and $y = 5$: $5>5\times0-7$, which is $5>-7$ (true).

Step2: Test option B (1, 1)

For $y\geq\frac{3}{10}x + 5$, substitute $x = 1$ and $y = 1$: $1\geq\frac{3}{10}\times1+5=\frac{3 + 50}{10}=5.3$, false.

Step3: Test option C (3, 8)

For $y\geq\frac{3}{10}x + 5$, substitute $x = 3$ and $y = 8$: $8\geq\frac{3}{10}\times3+5=\frac{9 + 50}{10}=5.9$ (true).
For $y>5x - 7$, substitute $x = 3$ and $y = 8$: $8>5\times3-7=15 - 7 = 8$, false ($8
ot>8$).

Step4: Test option D (10, 6)

For $y\geq\frac{3}{10}x + 5$, substitute $x = 10$ and $y = 6$: $6\geq\frac{3}{10}\times10+5=3 + 5=8$, false.

Answer:

A. $(0,5)$