Question

Which two ordered pairs are solutions for the inequality y>−2x+8 ? Algebra 1 Reference Sheet Link (2 points) Responses (2,−12) open paren 2 comma negative 12 close paren (−1,14) open paren negative 1 comma 14 close paren (4,2)

Answer 1

To determine which of the given ordered pairs are solutions for the inequality \( y > -2x + 8 \), we will plug in each ordered pair into the inequality and check if it holds true.

1. For the pair \( (2, -12) \):
\[
y = -12, \quad x = 2
\]
Substitute into the inequality:
\[
-12 > -2(2) + 8
\]
Simplifying the right side:
\[
-12 > -4 + 8
\]
\[
-12 > 4 \quad \text{(False)}
\]

2. For the pair \( (-1, 14) \):
\[
y = 14, \quad x = -1
\]
Substitute into the inequality:
\[
14 > -2(-1) + 8
\]
Simplifying the right side:
\[
14 > 2 + 8
\]
\[
14 > 10 \quad \text{(True)}
\]

3. For the pair \( (4, 2) \):
\[
y = 2, \quad x = 4
\]
Substitute into the inequality:
\[
2 > -2(4) + 8
\]
Simplifying the right side:
\[
2 > -8 + 8
\]
\[
2 > 0 \quad \text{(True)}
\]

Based on the checks above, the solutions for the inequality \( y > -2x + 8 \) are:
- \( (-1, 14) \)
- \( (4, 2) \)

So the two ordered pairs that are solutions for the inequality are \((-1, 14)\) and \((4, 2)\).