A1b Unit 8b Review

Front

What is a system of equations with no solution?

Back

A system of equations with no solution occurs when the lines represented by the equations are parallel, meaning they never intersect. Example: 5x + y = 6 and 5x + y = -6.

Front

What is set builder notation?

Back

Set builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy. Example: {x | x < -11}.

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set. Example: For the inequality 5 ≥ x, the line is solid.

Front

What is the solution to the system of equations 3x = 2y + 6 and 5x + 7y = 41?

Back

The solution is (4, 3).

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other. Example: x > 5.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 2 means x is any number less than 2.

Front

What is the graphical representation of the inequality x < 1?

Back

The graphical representation is a number line with an open circle at 1 and a line extending to the left.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line and has an equal sign (e.g., y = 2x + 3), while a linear inequality represents a region of the plane and uses inequality signs (e.g., y < 2x + 3).