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 dashed boundary line.
the second inequality ( y geq 3.5x - 5 ) has a (\boldsymbol{\text{blank}}) boundary line.
both inequalities have a solution set that is (\boldsymbol{\text{blank}}) their boundary lines.
(\boldsymbol{\text{blank}}) is a point in the solution set of the system of inequalities.
(options: solid, dashed)

Explanation:

Step1: Analyze 2nd inequality boundary

The inequality $y \geq 3.5x - 5$ uses $\geq$, so its boundary line is solid (since equality is included).

Step2: Analyze solution set position

For $y > -2x + 3$, solutions lie above the boundary; for $y \geq 3.5x - 5$, solutions lie above the boundary. So both solution sets are above their boundary lines.

Step3: Identify a valid solution point

We need a point that satisfies both inequalities. Test $(2, 4)$:
For $y > -2x + 3$: $4 > -2(2)+3 = -1$, which is true.
For $y \geq 3.5x -5$: $4 \geq 3.5(2)-5 = 7-5=2$, which is true.

Answer:

1. solid
2. above
3. $(2, 4)$ (example valid point)