College Alg/Trig 8.5 Systems of Inequalities Name: ______
We have seen that equations in the form are graphs of a ______.
If we change = symbol to then we obtain a ______.
The solution to a linear system of inequalities is an ordered pair with the following property:
When you substitute the values for x and y, we obtain a ______.
Let’s decide whether the following are possible solutions to the linear system of inequalities:
Solution: Inequality:
Graphing Linear Inequalities:
1. Replace the inequality symbol with an ______and graph the corresponding line.(Remember if it is > or < we use a dashed line, but if it is we use a solid line.)
2. Choose a test point on either side of the line and ______.
Decide whether your result is true or false.
3. If your answer is true, shade in that direction. If your answer is false, shade in the opposite direction.
1. 2.
3. 4.
Graphing Systems of Linear Inequalities:
1. Graph each inequality. Shade appropriately.2. The solution is the region in which the two shaded regions overlap. Any point in this region will satisfy the system.
Examples: Solve each of the following system of inequalities by graphing.
#1.#2.
#3.#4.
#5..#6.
Write each sentence as a linear inequality in two variables
.1. The y-variable is at least more than the product of -2 and the x-variable.
2. The x-variable is at most 5 more than 3 times the y-variable.
3. The sum of the x-variable and the y-variable does not exceed 10.
Write a system of inequalities from the given statement.
4. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 4 and the x-variable does not exceed 6.
5. The sum of the x-variable and y-variable is at most more than 7. The y-variable added o the product of 5 and the x-variable does not exceed 10.
Write a system of inequalities for the dark region of each graph.
#6.#7.