Can someone help me with this problem I don't understand what to really do or even how to graph them I show what i have so far.
Directions: Solve each of the following systems of linear inequalities graphically.
Problem:
To graph a system of linear inequalities, follow these steps:
1. Write down both inequalities in standard form: Ax + By ≤ C.
2. Solve each inequality for y: y ≤ mx + b.
3. Identify the slope (m) and y-intercept (b) of each inequality.
4. Choose a convenient set of x-values and plug them into the inequality to find the corresponding y-values.
5. Plot the points on a graph and connect them with a dotted or solid line, depending on the inequality symbol (≤ or <).
6. Repeat steps 4 and 5 for the other inequality.
7. Determine the overlapping region, which represents the solution to the system of inequalities.
Now, let's look at an example problem and go through the steps together:
Problem:
Solve the following system of linear inequalities graphically:
1) 2x + y ≤ 4
2) y > -x - 2
Step 1: Write down the inequalities in standard form:
1) 2x + y ≤ 4
2) x + y > -2
Step 2: Solve each inequality for y:
1) y ≤ -2x + 4
2) y > -x - 2
Step 3: Identify the slope (m) and y-intercept (b) of each inequality:
1) Slope-intercept form: y = mx + b
- Inequality 1: y ≤ -2x + 4
- Slope: -2
- Y-intercept: 4
2) Slope-intercept form: y = mx + b
- Inequality 2: y > -x - 2
- Slope: -1
- Y-intercept: -2
Step 4: Choose x-values and find the corresponding y-values for each inequality.
- For inequality 1: Let's choose x = 0, 1, and 2.
- x = 0: y = -2(0) + 4 = 4
- x = 1: y = -2(1) + 4 = 2
- x = 2: y = -2(2) + 4 = 0
- For inequality 2: Let's choose x = -1, 0, and 1.
- x = -1: y = -(-1) - 2 = -1 - 2 = -3
- x = 0: y = -(0) - 2 = -2
- x = 1: y = -(1) - 2 = -3
Step 5: Plot the points on a graph and connect them with lines.
- For inequality 1: Plot the points (0, 4), (1, 2), and (2, 0). Connect them with a solid line because the inequality is "≤".
- For inequality 2: Plot the points (-1, -3), (0, -2), and (1, -3). Connect them with a dotted line because the inequality is ">".
Step 6: Determine the overlapping region on the graph.
- The overlapping region represents the solution to the system of inequalities.
I hope this helps! Let me know if you have any further questions.