can you guys please graph the system of inequalities and clasify the solution of
y¡Ü4x+4
y¡Ü-0.25x+4
y¡Ý4x-1
y¡Ý-0.25x-1
To graph the system of inequalities and classify the solutions, follow these steps:
Step 1: Graph the first inequality, y ≤ 4x + 4:
- Start by graphing the line y = 4x + 4. This line has a slope of 4 and a y-intercept of 4.
- Since we have a less than or equal to (≤) inequality, we need to shade the region below the line. You can shade it with vertical lines or by coloring the region.
Step 2: Graph the second inequality, y ≤ -0.25x + 4:
- Start by graphing the line y = -0.25x + 4. This line has a slope of -0.25 and a y-intercept of 4.
- Shade the region below the line.
Step 3: Graph the third inequality, y ≥ 4x - 1:
- Start by graphing the line y = 4x - 1. This line has a slope of 4 and a y-intercept of -1.
- Shade the region above the line.
Step 4: Graph the fourth inequality, y ≥ -0.25x - 1:
- Start by graphing the line y = -0.25x - 1. This line has a slope of -0.25 and a y-intercept of -1.
- Shade the region above the line.
Step 5: Analyze the graph and classify the solution:
- Examine the shaded region where all the inequalities overlap. This region represents the solution of the system of inequalities.
- In this case, the overlapping region is the shaded region in the middle, bounded by the lines y = 4x - 1 and y = -0.25x + 4.
- Since all four inequalities are non-strict (contain "≤" or "≥"), the solution also includes the lines themselves.
- Therefore, the solution is the area between the lines y = 4x - 1 and y = -0.25x + 4, including the lines.
Note: It may be helpful to use different colors or patterns to shade the regions for a clear visual representation of the solution.