Transcript Solving Systems of Linear Inequalities

Chapter 7
Section 6: Solving Systems of Linear Inequalities
In this section, we will…
Determine if a given ordered pair is a solution to a linear inequality or to a
system of linear inequalities
Solve a linear inequality
Solve a system of linear inequalities
Solve applications
In chapter 2, we solved equations and inequalities in one-variable:
equation:
x2
inequalities:
x2
x2
Now we will solve equations and inequalities in two-variables:
equation:
inequalities:
y  13 x  2
y  13 x  2
y  13 x  2
Example: Determine if  2,0  is a solution of x  4 y  1
Example: Determine if  2, 14  is a solution of x  4 y  1
Example: A linear inequality has been graphed. Determine if the given
points satisfy the inequality.
 4,6
 3,1
Example: A linear inequality has been graphed. Determine if the given
points satisfy the inequality.
 4, 6
 3,1
Solving Linear Inequalities Graphically
1. Graph the boundary line.
• Solve the inequality for y
*** Remember to flip the sign if you multiply
or divide both sides by a negative number ***
• Graph using the slope and y-intercept
• Solid line if  or 
• Dashed line if < or >
2. Determine which side of the boundary line to shade.
• Pick a test point that does not fall on the boundary line
• True statement – shade that side
• False statement – shade the other side
Example: Solve the linear inequality by graphing.
y  3x
Example: Solve the linear inequality by graphing.
3x  2 y  6
Example: Solve the linear inequality by graphing.
y  3
We will now solve systems of linear inequalities.
Solving Systems Linear Inequalities Graphically
1. For each inequality: graph the boundary line.
• Solve the inequalities for y
*** Remember to flip the sign if you multiply
or divide both sides by a negative number ***
• Graph each using the slope and y-intercept
• Solid line if  or 
• Dashed line if < or >
2. For each inequality: determine which side of the boundary line to shade.
• For each: pick a test point that does not fall on the boundary line
• True statement – shade that side
• False statement – shade the other side
3. Clearly indicate the solution for the system (where the solution sets overlap)
Example: Solve the system of linear equations by graphing.
2 x  y  3

 x  2 y  1
Example: Solve the system of linear equations by graphing.
3x  y  2

 y  3(1  x)
Example: Match each equation, inequality or system with its graph.
x y 2
x y 2
x  y  2

x  y  2
x  y  2

x  2  2