Unit 4 Test Review

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that share the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality.

Front

What does the solution (1,-2) represent in a system of equations?

Back

The solution (1,-2) represents the point where the two lines intersect, meaning that x=1 and y=-2 satisfy both equations in the system.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the budget constraint in a word problem?

Back

The budget constraint is an inequality that represents the limit on spending based on available funds. It typically involves the costs of items and the total budget.

Front

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

Back

The shaded region represents all possible solutions that satisfy the inequalities. Any point within this region is a valid solution.

Front

How do you write an inequality from a word problem?

Back

Identify the variables, determine the relationship between them, and express the constraints using inequality symbols based on the context.

Front

Back

This inequality represents the total cost of items (where x is the number of balloons and y is the number of streamers) that must not exceed $30.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included (< or >).

Front

What is a feasible region in linear programming?

Back

The feasible region is the area on a graph that satisfies all constraints of a linear programming problem, representing all possible solutions.