Question

Which of the points on the graph is a solution for the simultaneous inequalities y > 4x − 2 and y ≥ −13x + 2 ?

(1 point)
(
,
)

Answer 1

I don’t have the graph or the list of candidate points, so I can’t pick the specific point. Please either describe the points (their coordinates) or upload the graph.

How to check any given point (x,y):
1. Plug into y > 4x − 2. If y is strictly greater than 4x − 2, that inequality is satisfied.
2. Plug into y ≥ −13x + 2. If y is greater than or equal to −13x + 2, that inequality is satisfied.
A point is a solution only if it satisfies both.

Useful facts you can use to narrow choices:
- The two lines meet at x = 4/17, y = −18/17 (approximately x ≈ 0.2353, y ≈ −1.0588).
- For x > 4/17 the requirement reduces to y > 4x − 2 (the 4x−2 line is the higher one there).
- For x < 4/17 the requirement reduces to y ≥ −13x + 2 (the −13x+2 line is the higher one there).

Example: (0,2)
- Check y > 4x − 2: 2 > −2 → true.
- Check y ≥ −13x + 2: 2 ≥ 2 → true.
So (0,2) would be a solution.

Send the candidate points (or the image) and I’ll mark which one(s) satisfy both inequalities.