Alg 1 Ch 5 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 if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The lines represented by the equations are identical, meaning they overlap completely.

Front

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

Back

Substitute the point's coordinates into each equation; if they satisfy all equations, it is a solution.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of a boundary line, which can be solid or dashed depending on the inequality.

Front

What does a dashed line represent in a graph of an inequality?

Back

It indicates that points on the line are not included in the solution set (for 'less than' or 'greater than').

Front

What does a solid line represent in a graph of an inequality?

Back

It indicates that points on the line are included in the solution set (for 'less than or equal to' or 'greater than or equal to').

Front

What is the boundary line in a system of inequalities?

Back

The line that separates the solution region from the non-solution region.

Front

How do you find the intersection point of two lines?

Back

Solve the system of equations formed by the two lines simultaneously.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.