Solving Systems of Inequalities

Front

What does it mean to isolate a variable in an equation or inequality?

Back

To get the variable by itself on one side of the equation or inequality.

Front

What is the inequality represented by the line with a solid line and shading above?

Back

y ≥ mx + b (where m is the slope and b is the y-intercept).

Front

What does a dashed line indicate in the graph of an inequality?

Back

It indicates that the points on the line are not included in the solution (e.g., y < mx + b).

Front

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

Back

Substitute the point into each inequality; if it satisfies all inequalities, it is a solution.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line (not including the line), while 'y ≤ mx + b' uses a solid line (including the line).

Front

What does the solution set of a system of inequalities represent?

Back

It represents all the points that satisfy all inequalities in the system.

Front

What is the graphical representation of the inequality 'y > 2x - 3'?

Back

A dashed line for y = 2x - 3 with shading above the line.

Front

How can you check if a point (x, y) is a solution to the inequality 'y < -x + 4'?

Back

Substitute x and y into the inequality; if the inequality holds true, then it is a solution.

Front

What does it mean if two inequalities are graphed and their shaded regions overlap?

Back

The overlapping region represents the solution set for the system of inequalities.

Front

What is the significance of the y-intercept in the inequality 'y ≤ 3x + 2'?

Back

The y-intercept (0, 2) is the point where the line crosses the y-axis.