Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

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

Back

It means the system has no solution because the lines never intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is 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 for the other.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the appropriate region based on the inequality.

Front

What does a dashed line indicate in graphing inequalities?

Back

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

Front

What does a solid line indicate in graphing inequalities?

Back

It indicates that the points on the line are included in the solution set.