Systems of Equations/Inequalities

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 that the equations intersect at exactly one point.

Front

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

Back

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

Front

What does it mean for a system of equations 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

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

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

Front

What is a boundary line in the context of inequalities?

Back

A line that represents the boundary of the solution set for a linear inequality.

Front

Are points on the boundary line included in the solution set for a 'less than or equal to' inequality?

Back

Yes, points on the boundary line are included in the solution set.

Front

What is the graphical representation of a system of equations with intersecting lines?

Back

The lines cross at a single point, which is the unique solution to the system.