Systems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system to have one solution?

Back

It means that the equations intersect at exactly one point on a graph.

Front

What does it mean for a system to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean for a system to have infinitely many solutions?

Back

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

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or equal to the other.

Front

How do you graph an inequality?

Back

By shading the region of the graph that satisfies the inequality and using a dashed or solid line to indicate whether the boundary is included.

Front

What is a solution to a system of inequalities?

Back

A set of values that satisfies all inequalities in the system.