Question

graphing solution sets
solve the system of inequalities: ( y + 2x > 3 ) and ( y geq 3.5x - 5 )
the first inequality, ( y + 2x > 3 ), is ( y > -2x + 3 ) in slope - intercept form.
the first inequality, ( y + 2x > 3 ), has a (\boldsymbol{\text{dropdown}}) boundary line.
the second inequality, ( y geq 3.5x - 5 ), (\boldsymbol{\text{dropdown}}) boundary line
both inequalities have a solution set (\boldsymbol{\text{dropdown}}) their boundary lines.
(\boldsymbol{\text{dropdown}}) is a point in the solution set of the system of inequalities.
(options for dropdowns: solid, dashed)

Explanation:

Step1: Analyze first inequality boundary

The inequality $y + 2x > 3$ (or $y > -2x + 3$) uses $>$, so its boundary line is not included. This means it is a dashed boundary line.

Step2: Analyze second inequality boundary

The inequality $y \geq 3.5x - 5$ uses $\geq$, so its boundary line is included. This means it is a solid boundary line.

Step3: Match solution set to boundaries

For $y > -2x + 3$, the solution set is shaded above its dashed boundary line. For $y \geq 3.5x - 5$, the solution set is shaded above its solid boundary line. The overall solution set is the overlap of these two regions. A sample point in the solution set (e.g., $(0,4)$) satisfies both: $4 + 2(0) = 4 > 3$ and $4 \geq 3.5(0) - 5 = -5$.

Answer:

The first inequality, $y + 2x > 3$, has a $\boldsymbol{dashed}$ boundary line.
The second inequality, $y \geq 3.5x - 5$, has a $\boldsymbol{solid}$ boundary line.
Both inequalities have a solution set shaded $\boldsymbol{above}$ their boundary lines.
$\boldsymbol{(0, 4)}$ is a point in the solution set of the system of inequalities.