Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as if it were an equality. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the region that satisfies the inequality.

Front

What does the symbol '>' mean in an inequality?

Back

'>' means that the value on the left is greater than the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means that the value on the left is less than or equal to the value on the right.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all the possible solutions that satisfy the inequality.

Front

What is the first step in solving a system of inequalities?

Back

The first step is to graph each inequality on the same coordinate plane.

Front

How do you rewrite the inequality 3x - 6y > 12 in 'y=' form?

Back

y < (1/2)x - 2.

Front

What type of line is used when graphing y ≤ mx + b?

Back

A solid line is used because the inequality includes '≤'.

Front

What is the solution to the inequality y > x + 1?

Back

The solution is the region above the line y = x + 1.