I have a problem, which requires I solve the following system of linear inequality graphically.
my textbook is vague and does not provide online examples or instruction to assist me withinfo to work the problem. Please help? Thank you.
3x - y is lessor than or equal to 6
x is greater than or equal 1
y is lessor than or equal 3
x=3
y=2
no cause 3x3-2=7 not 6
does this help much???
To solve this system of linear inequalities graphically, you need to plot the individual inequalities on a graph to determine the feasible region where all the conditions are satisfied.
Let's start with the first inequality: 3x - y ≤ 6. To graph this, we can first simplify it by rearranging it to the form y ≥ 3x - 6.
1. Plot the line y = 3x - 6 on the graph. To do this, select a few x-values and substitute them into the equation to find the corresponding y-values. For example, if x = 0, then y = 3(0) - 6 = -6. We can find two more points using different x-values, such as x = 1 and x = 2. Plot these points and draw a straight line passing through them.
2. Since the inequality is y ≥ 3x - 6, shade the area above the line (including the line itself) to represent all the possible points that satisfy the inequality.
Next, let's move to the second inequality: x ≥ 1. This is a simple vertical line that passes through x = 1. Plot this line and shade the area to the right of the line to represent the points that satisfy the condition x ≥ 1.
Finally, consider the third inequality: y ≤ 3. This is a horizontal line that passes through y = 3. Plot this line and shade the area below the line to represent the points that satisfy the condition y ≤ 3.
Now, all that is left is to identify the region where all three conditions overlap. This overlapping region represents the solution to the system of inequalities. In this case, it would be the area that is shaded below the y ≤ 3 line, above the y ≥ 3x - 6 line, and to the right of the x ≥ 1 line.
You can then write down your solution based on the graph you've drawn. For example, you could describe it as "x is greater than or equal to 1, y is less than or equal to 3, and y is greater than or equal to 3x - 6."
Remember to label your axes appropriately and use a ruler or graphing software to create accurate plots.