Question

solve the system of two linear inequalities graphically.\

$$\begin{cases}8y - 8x > 32\\\\y > 1\\end{cases}$$

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step 3 of 3 : graph the solution set for the system.\
answer

Explanation:

Step1: Simplify first inequality

Rearrange to slope-intercept form:
$$8y - 8x > 32$$
Divide by 8: $y - x > 4$, so $y > x + 4$

Step2: Identify boundary lines

• For $y > x + 4$: Boundary is $y = x + 4$, dashed line (since $>$), shade above the line.
• For $y > 1$: Boundary is $y = 1$, dashed line (since $>$), shade above the line.

Step3: Find overlapping shaded region

The solution set is the area that is shaded above both dashed lines $y = x + 4$ and $y = 1$.

Answer:

The solution is the region above both the dashed line $y = x + 4$ and the dashed line $y = 1$. This overlapping shaded area represents all $(x,y)$ pairs that satisfy both inequalities.