Question

1. graph the system. identify a solution if possible.

y < x - 1
y ≥ x + 1

Explanation:

Step1: Analyze the two inequalities

The first inequality is \( y < x - 1 \), which represents the region below the line \( y = x - 1 \) (the line is dashed because the inequality is strict, \( < \)). The second inequality is \( y \geq x + 1 \), which represents the region above or on the line \( y = x + 1 \) (the line is solid because the inequality is \( \geq \)).

Step2: Check for overlapping regions

The line \( y = x - 1 \) has a slope of 1 and a y - intercept of - 1. The line \( y = x + 1 \) has a slope of 1 and a y - intercept of 1. Since both lines have the same slope (they are parallel) and different y - intercepts, the region below \( y = x - 1 \) and the region above or on \( y = x + 1 \) do not overlap.

Answer:

There is no solution to this system of inequalities because the regions defined by \( y < x - 1 \) and \( y \geq x + 1 \) (which are bounded by parallel lines) do not overlap.