Systems of Linear Inequalities

Systems of Linear Inequalities

Graphing a Linear Inequality

Solve the inequality for y, then graph y = mx + b.

y > mx + b is satisfied above the line.y = mx + b is satisfied on the line itself.y < mx + b is satisfied below the line.

Example:

Graph the following:

y > x + 12y < x 23x 2y 6

Graphing a Linear Inequality

If the inequality involves x and not y, then graph the vertical line x = k.

x > k is satisfied to the right of the line.x = k is satisfied on the line itself.x < k is satisfied to the left of the line.

Graphing a Linear Inequality

If the inequality involves y and not x, then graph the horizontal line y = k.

y > k is satisfied above the line.y = k is satisfied on the line itself.y < k is satisfied below the line.

Example:

Graph the following:

x > 4y 5

Solving Systems of Linear Inequalities

Graphical Method

To solve systems of two linear inequalities graphically, graph each of the linear inequalities on the same coordinate plane.The region that is common to the inequalities is the solution set of the system.

Example:

Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.1. 3.

2. 4.

Example:

Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.5. 6.

Exercises:

Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.1. 3.

2. 4.

Exercises:

Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.5. 6. 7.

Exercises:

Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.8. 9. 10.