[tex]\boxed{y\geq 3x-2, \ x+2y\leq 4}[/tex]
Explanation:
First of all, we need to know the equations of the given lines. According to the options the equations of the lines are:
1. First equation: Written in Slope-Intercept Form:
[tex]y=3x-2[/tex]
2. Second equation: Written in Standard Form:
[tex]x+2y=4[/tex]
According to the graph, both lines are dashed meaning both inequalities must include either ≥ or ≤. So let's taste a point on the coordinate system in order to know which option is satisfied:
Hence, let's take point (0, 0):
[tex]y \ (?) \ 3x-2 \\ \\ 0 \ (?) \ 3(0)-2 \\ \\ 0 \ (?) \ -2 \\ \\ \\ So \ 0 \ is \ greater \ than \ -2: \\ \\ 0\geq 2 \\ \\ \\ \\ x+2y \ (?) \ 4 \\ \\ 0+2(0) \ (?) \ 4 \\ \\ 0 \ (?) \ 4 \\ \\ \\ So \ 0 \ is \ less \ than \ 4: \\ \\ 0\leq 4[/tex]
Therefore, the correct option is:
[tex]\boxed{y\geq 3x-2, \ x+2y\leq 4}[/tex]
Learn more:
System of inequalities: https://brainly.com/question/12890742
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