Solutions to 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 graphs of the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, overlapping completely.

Front

How can you determine the solution to a system of equations graphically?

Back

By finding the point where the graphs of the equations intersect.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point, indicating one solution.

Front

What is the graphical representation of parallel lines?

Back

Two lines that never meet, indicating no solution.

Front

What is the graphical representation of the same line?

Back

A single line that represents infinitely many solutions.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract equations to eliminate one variable, making it easier to solve.