Question

Which system of linear inequalities is graphed?

y
<
−
x
+
5
y
>
6
x
−
4
y
≤
−
x
+
5
y
≥
6
x
−
4
y
>
−
x
+
5
y
>
6
x
−
4

y
>
−
x
+
5
y
≥
6
x
−
4

Answer 1

Answer:y < -x+5 and y > 6x-4

Explanation:

Answer 2

Answer: y < -x+5 and y > 6x-4

Reason:

The green dashed boundary line goes through (0,5) and (5,0)

Use the slope formula to find the slope is m = -1

Use the point-slope equation to find the equation of the boundary line is y = -x+5

Since we're below this boundary line, we change the equal sign to a less than sign.

Therefore, the green shaded region is represented by y < -x+5

If the boundary was solid, then you use "or equal to" as part of the inequality sign. But in this case, points on the boundary are not part of the solution set.

Through similar steps you should find that the purple region is represented by the inequality y > 6x-4

Note that the purple shaded region is above its corresponding boundary line. So we use "greater than" instead of "less than".