Review: Inequalities and Systems

Front

What does it mean when a system of equations has no solutions?

Back

It means that the lines representing the equations are parallel, having the same slope but different y-intercepts.

Front

What is the significance of a dotted line in an inequality graph?

Back

A dotted line indicates that the points on the line are not included in the solution set.

Front

Which point is a solution to the inequality y < 2x + 3?

Back

(1, 0) is a solution because it satisfies the inequality.

Front

How do you solve a system of equations using elimination?

Back

You eliminate one variable by adding or subtracting the equations to find the value of the other variable.

Front

What does it mean for two lines to have the same slope?

Back

It means that the lines are parallel and will never intersect, resulting in no solutions for the system of equations.

Front

What is the solution to the system of equations 3x + y = 19 and 2x - y = 6?

Back

The solution is (5, 4).

Front

How can you determine if a point is a solution to an inequality?

Back

Substitute the point into the inequality; if the inequality holds true, then the point is a solution.

Front

What is the graphical representation of the inequality y ≥ 2x - 1?

Back

The graph includes a solid line for y = 2x - 1 and the region above the line.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and every point on the line is a solution.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution, while a dotted line indicates they are not.