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 solid boundary line.
both inequalities have a solution set that is shaded above their boundary lines.
______ is a point in the solution set of the system of inequalities.
((-2, 2))
((0, 0))
((1, 5))
((3, 1))

Explanation:

Step1: Test point (-2,2) in first inequality

Substitute $x=-2, y=2$ into $y+2x>3$:
$2 + 2(-2) = 2 - 4 = -2$
$-2 > 3$ is false.

Step2: Test point (0,0) in first inequality

Substitute $x=0, y=0$ into $y+2x>3$:
$0 + 2(0) = 0$
$0 > 3$ is false.

Step3: Test point (1,5) in both inequalities

First inequality: $5 + 2(1) = 7$, $7 > 3$ is true.
Second inequality: Substitute into $y \geq 3.5x -5$:
$5 \geq 3.5(1) -5 = 3.5 -5 = -1.5$
$5 \geq -1.5$ is true.

Step4: Test point (3,1) in second inequality

Substitute $x=3, y=1$ into $y \geq 3.5x -5$:
$1 \geq 3.5(3) -5 = 10.5 -5 = 5.5$
$1 \geq 5.5$ is false.

Answer:

(1, 5)