question 11 of 12 (1 point) | question attempt: 1 of unlimited\ny ≤ 5x - 4\ny > -2x + 7\nyour answer

Explanation:

Step1: Analyze ( y \leq 5x - 4 )

The inequality ( y \leq 5x - 4 ) represents a line with slope ( 5 ) and y - intercept ( - 4 ). Since the inequality is "less than or equal to", we draw a solid line (because the points on the line are included in the solution set) and shade the region below the line.

Step2: Analyze ( y > - 2x + 7 )

The inequality ( y > - 2x + 7 ) represents a line with slope ( - 2 ) and y - intercept ( 7 ). Since the inequality is "greater than", we draw a dashed line (because the points on the line are not included in the solution set) and shade the region above the line.

Step3: Find the intersection

The solution to the system of inequalities is the region that is shaded by both inequalities. To graph the system:

• For ( y = 5x - 4 ), when ( x = 0 ), ( y=-4 ); when ( y = 0 ), ( 5x-4=0\Rightarrow x=\frac{4}{5} = 0.8 ). Plot the points ( (0,-4) ) and ( (0.8,0) ) and draw a solid line through them, then shade below the line.
• For ( y=-2x + 7 ), when ( x = 0 ), ( y = 7 ); when ( y=0 ), ( - 2x+7=0\Rightarrow x = 3.5 ). Plot the points ( (0,7) ) and ( (3.5,0) ) and draw a dashed line through them, then shade above the line.
• The overlapping region of the two shaded areas is the solution to the system of inequalities.

Answer:

To graph the system ( \begin{cases}y\leq5x - 4\y>-2x + 7\end{cases} ):

1. Draw a solid line for ( y = 5x-4 ) (slope ( 5 ), y - intercept ( - 4 )) and shade below it.
2. Draw a dashed line for ( y=-2x + 7 ) (slope ( - 2 ), y - intercept ( 7 )) and shade above it.
3. The solution is the region that is shaded by both, i.e., the region that is below the solid line ( y = 5x-4 ) and above the dashed line ( y=-2x + 7 ).