Question

(graphing systems of inequalities lc)
a system of inequalities is shown on the graph.
graph of a system of inequalities with two lines: y > x + 1 and y ≤ 5x - 3, and a shaded region
which coordinate pair is a solution to the system of inequalities?
○ (1, 2)
○ (0, 1)
○ (0, -3)
○ (2, 4)

Explanation:

Step1: Check (1,2) in inequalities

For \( y > x + 1 \): \( 2 > 1 + 1 \) → \( 2 > 2 \)? No. So (1,2) is out.

Step2: Check (0,1) in inequalities

For \( y > x + 1 \): \( 1 > 0 + 1 \) → \( 1 > 1 \)? No. So (0,1) is out.

Step3: Check (0, -3) in inequalities

For \( y > x + 1 \): \( -3 > 0 + 1 \) → \( -3 > 1 \)? No. So (0, -3) is out.

Step4: Check (2,4) in inequalities

For \( y > x + 1 \): \( 4 > 2 + 1 \) → \( 4 > 3 \), Yes.
For \( y \leq 5x - 3 \): \( 4 \leq 5(2) - 3 \) → \( 4 \leq 10 - 3 \) → \( 4 \leq 7 \), Yes.

Answer:

(2, 4)