Question

which graph shows the solution to the system of linear inequalities?
y ≤ 2x - 5
y > -3x + 1

Explanation:

Step1: Analyze first inequality

The inequality is $y \leq 2x - 5$.

1. First, identify the boundary line: $y = 2x - 5$. This is a straight line with slope $2$ and y-intercept $-5$.
2. The $\leq$ symbol means the line is solid (includes points on the line), and we shade below the line (since $y$ is less than or equal to the expression).

Step2: Analyze second inequality

The inequality is $y > -3x + 1$.

1. Identify the boundary line: $y = -3x + 1$. This is a straight line with slope $-3$ and y-intercept $1$.
2. The $>$ symbol means the line is dashed (does not include points on the line), and we shade above the line (since $y$ is greater than the expression).

Step3: Find overlapping region

The solution to the system is the area where the shaded regions from Step1 and Step2 overlap.
To verify, we can test a point in the potential overlap, e.g., $(2, -1)$:

• For $y \leq 2x -5$: $-1 \leq 2(2)-5 = -1$, which is true.
• For $y > -3x +1$: $-1 > -3(2)+1 = -5$, which is true.

Answer:

The correct graph will have:

1. A solid line $y=2x-5$ with shading below it
2. A dashed line $y=-3x+1$ with shading above it
3. The overlapping shaded region (where both shadings meet) as the solution area.