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 if a system of equations has one solution?

Back

The lines represented by the equations intersect at exactly one point.

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 the same line, overlapping each other.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By analyzing the intersection points of the lines on a graph.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point on a graph.

Front

What is the graphical representation of parallel lines?

Back

Two lines that run alongside each other and never meet.

Front

What is the solution to the system of equations 3x + 2y = 315 and 2x + 4y = 450?

Back

(1, -1) is not the solution; the correct solution is (45 minutes for a haircut).

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.