Systems Checkpoint (all 3 methods)

Front

What is a system of linear equations?

Back

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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

Solve for x and y using elimination: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)

Front

Solve for x and y using substitution: y = 4x + 1 and 3x + 2y = 13.

Back

(1, 5)

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.