Question

in 1-3, graph the system of ine solution to the system.
1
$y < 5$
$y \geq \frac{1}{3}x + 3$
grid graph
a. $(-3, 4)$
b. $(2, 5)$

Explanation:

Step1: Analyze Inequality \( y < 5 \)

For a point \((x,y)\) to satisfy \( y < 5 \), its \( y \)-coordinate must be less than 5.

• For point a \((-3, 4)\): \( 4 < 5 \), which is true.
• For point b \((2, 5)\): \( 5 < 5 \) is false (since it's equal, not less).

Step2: Analyze Inequality \( y \geq \frac{1}{3}x + 3 \)

Substitute \( x = -3 \), \( y = 4 \) into \( y \geq \frac{1}{3}x + 3 \):
\( 4 \geq \frac{1}{3}(-3) + 3 \)
\( 4 \geq -1 + 3 \)
\( 4 \geq 2 \), which is true.

Substitute \( x = 2 \), \( y = 5 \) into \( y \geq \frac{1}{3}x + 3 \):
\( 5 \geq \frac{1}{3}(2) + 3 \)
\( 5 \geq \frac{2}{3} + 3 = \frac{11}{3} \approx 3.67 \), which is true, but we already saw \( y = 5 \) fails \( y < 5 \).

Answer:

a. \((-3, 4)\)