which statements are true about the graph of the system of linear inequalities? select two options.\ny > 3x…

Explanation:

Step1: Analyze $y>3x - 4$

For $y>3x - 4$, the inequality is strict ($>$), so the line $y = 3x-4$ is dashed, and since $y$ is greater, the shading is above the line.

Step2: Analyze $y\leq\frac{1}{2}x + 1$

For $y\leq\frac{1}{2}x + 1$, the inequality is non - strict ($\leq$), so the line $y=\frac{1}{2}x + 1$ is solid, and since $y$ is less than or equal, the shading is below the line.

Step3: Check for intersection

The slopes of the lines $y = 3x-4$ and $y=\frac{1}{2}x + 1$ are different ($3\neq\frac{1}{2}$), so their graphs will intersect.

Step4: Check y - axis intersection

For $y>3x - 4$, when $x = 0$, $y>- 4$. For $y\leq\frac{1}{2}x + 1$, when $x = 0$, $y\leq1$. The intersection points with the $y$-axis are $(0,-4)$ (for the boundary of $y>3x - 4$) and $(0,1)$ (for the boundary of $y\leq\frac{1}{2}x + 1$). Also, there are solutions to the system as the graphs intersect.

Answer:

The graph of $y>3x - 4$ has shading above a dashed line. The graphs of the inequalities will intersect.