Question

1. $y < -5x + 6$

$y \geq 2x - 1$

Explanation:

Step1: Find intersection of the two lines

Set $-5x + 6 = 2x - 1$
$6 + 1 = 2x + 5x$
$7 = 7x$
$x = 1$
Substitute $x=1$ into $y=2x-1$: $y=2(1)-1=1$
Intersection point: $(1,1)$

Step2: Graph $y < -5x + 6$

• Identify intercepts:

x-intercept: set $y=0$, $0=-5x+6 \Rightarrow x=\frac{6}{5}=1.2$
y-intercept: set $x=0$, $y=6$

• Draw a dashed line through $(1.2,0)$ and $(0,6)$
• Shade the region below the line (since $y <$)

Step3: Graph $y \geq 2x - 1$

• Identify intercepts:

x-intercept: set $y=0$, $0=2x-1 \Rightarrow x=\frac{1}{2}=0.5$
y-intercept: set $x=0$, $y=-1$

• Draw a solid line through $(0.5,0)$ and $(0,-1)$
• Shade the region above the line (since $y \geq$)

Step4: Identify solution region

The solution is the overlapping shaded area, bounded above by the dashed line $y=-5x+6$, below by the solid line $y=2x-1$, and to the left/right up to the intersection point $(1,1)$.

Answer:

The solution is the overlapping shaded region:

1. Dashed line for $y=-5x+6$ (shade below it)
2. Solid line for $y=2x-1$ (shade above it)
3. Overlap is the area bounded by these lines, with intersection point $(1,1)$