Question

1. select all the ordered pairs that are solutions to the system of inequalities.

$y \geq 3 - 2x$
$y > x - 5$
a. $(1, -1)$ d. $(4, 2)$
b. $(3, 1)$ e. $(4, -3$
c. $(2, 5)$

Explanation:

Step1: Check Option A (1, -1)

Substitute \(x = 1\), \(y=-1\) into \(y\geq3 - 2x\):
\(-1\geq3-2(1)\) → \(-1\geq1\), which is false. So A is not a solution.

Step2: Check Option B (3, 1)

Substitute \(x = 3\), \(y = 1\) into \(y\geq3 - 2x\):
\(1\geq3-2(3)\) → \(1\geq - 3\) (true).
Substitute into \(y>x - 5\):
\(1>3 - 5\) → \(1>-2\) (true). So B is a solution.

Step3: Check Option C (2, 5)

Substitute \(x = 2\), \(y = 5\) into \(y\geq3 - 2x\):
\(5\geq3-2(2)\) → \(5\geq - 1\) (true).
Substitute into \(y>x - 5\):
\(5>2 - 5\) → \(5>-3\) (true). So C is a solution.

Step4: Check Option D (4, 2)

Substitute \(x = 4\), \(y = 2\) into \(y\geq3 - 2x\):
\(2\geq3-2(4)\) → \(2\geq - 5\) (true).
Substitute into \(y>x - 5\):
\(2>4 - 5\) → \(2>-1\) (true). So D is a solution.

Step5: Check Option E (4, -3)

Substitute \(x = 4\), \(y=-3\) into \(y\geq3 - 2x\):
\(-3\geq3-2(4)\) → \(-3\geq - 5\) (true).
Substitute into \(y>x - 5\):
\(-3>4 - 5\) → \(-3>-1\) (false). So E is not a solution.

Answer:

B. (3, 1), C. (2, 5), D. (4, 2)