Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward your grade.
graph the system to determine which of the following points represents a solution to the system.
$y \geq -\frac{1}{3}x - 4$
$y < 2x - 5$
$x < 4$
(1 point)
\\(\circ\\) (4, 3)
\\(\circ\\) (3, -3)
\\(\circ\\) (4, -6)
\\(\circ\\) (3, 1)

Explanation:

Step1: Check \( x < 4 \)

For \((4,3)\): \( 4 < 4 \) is false.
For \((3,-3)\): \( 3 < 4 \) is true.
For \((4,-6)\): \( 4 < 4 \) is false.
For \((3,1)\): \( 3 < 4 \) is true.

Step2: Check \( y \geq -\frac{1}{3}x - 4 \)

For \((3,-3)\):
\( -\frac{1}{3}(3) - 4 = -1 - 4 = -5 \)
\( -3 \geq -5 \) is true.

For \((3,1)\):
\( -\frac{1}{3}(3) - 4 = -5 \)
\( 1 \geq -5 \) is true.

Step3: Check \( y < 2x - 5 \)

For \((3,-3)\):
\( 2(3) - 5 = 6 - 5 = 1 \)
\( -3 < 1 \) is true.

For \((3,1)\):
\( 2(3) - 5 = 1 \)
\( 1 < 1 \) is false.

Answer:

\((3, -3)\) (Option: \(\boldsymbol{(3, -3)}\))