Honors Algebra - Unit 5 Review - Systems of Equations 2024

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 region where the graphs of the inequalities overlap.

Front

How do you graph an inequality like y > x - 2?

Back

To graph y > x - 2, first graph the line y = x - 2 as a dashed line (since it's not inclusive). Then shade the area above the line.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value can be less than or equal to a certain number.

Front

How do you find the intersection point of two lines represented by equations?

Back

To find the intersection point, solve the equations simultaneously, either by substitution or elimination methods.

Front

What is the significance of the solution to a system of equations?

Back

The solution to a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.

Front

What is the first step in solving a word problem involving systems of equations?

Back

The first step is to define the variables that represent the unknown quantities in the problem.

Front

How can you determine if a point satisfies a system of inequalities?

Back

To determine if a point satisfies a system of inequalities, substitute the point's coordinates into each inequality and check if all inequalities hold true.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating that there is no solution to the system.

Front

What is the graphical representation of the inequality y < 3x?

Back

The line y = 3x is drawn as a dashed line, and the area below the line is shaded to represent all points where y is less than 3x.

Front

How do you interpret the solution of a system of inequalities graphically?

Back

The solution of a system of inequalities is represented by the shaded region where all inequalities overlap on the graph.