Question

1. $y < |x - 5|$

$2x - y > 1$

Explanation:

Step1: Rewrite inequalities to slope-intercept form

First inequality: $y < |x - 5|$ (already in usable form for absolute value graph)
Second inequality: Rearrange $2x - y > 1$ to $y < 2x - 1$

Step2: Graph boundary lines

1. For $y = |x - 5|$: This is a V-shaped absolute value graph with vertex at $(5, 0)$. The lines are $y = x - 5$ (for $x \geq 5$) and $y = -x + 5$ (for $x < 5$). Draw this as a dashed line (since the inequality is $<$).
2. For $y = 2x - 1$: This is a straight line with slope $2$ and y-intercept $(0, -1)$. Draw this as a dashed line (since the inequality is $<$).

Step3: Shade solution regions

1. For $y < |x - 5|$: Shade the area below the V-shaped graph.
2. For $y < 2x - 1$: Shade the area below the straight line.
3. The final solution is the overlapping shaded region of the two inequalities.

Step4: Identify intersection point of boundaries

Set $2x - 1 = x - 5$ (for $x \geq 5$, no solution here)
Set $2x - 1 = -x + 5$:
$2x + x = 5 + 1$
$3x = 6$
$x = 2$
Substitute $x=2$ into $y = 2x -1$: $y = 2(2) -1 = 3$
Intersection point is $(2, 3)$

Answer:

The solution is the overlapping shaded region below both the dashed V-shaped graph $y=|x-5|$ and the dashed line $y=2x-1$, bounded by their intersection at $(2, 3)$.