System of Equations (Graphing and Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean if two lines intersect on a graph?

Back

It means that the system of equations has one unique solution.

Front

What is the graphical representation of a system of equations with no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you solve a system of equations by substitution?

Back

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

Front

What is the solution to the system of equations: y = 2x + 3 and y = -x + 1?

Back

(1, 5) is the solution.

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope is 4.

Front

What does the term 'parallel lines' indicate in a system of equations?

Back

It indicates that the system has no solution because the lines never meet.

Front

What is the first step in graphing a system of equations?

Back

Identify the y-intercept and slope of each equation.

Front

What does it mean if two lines are the same line on a graph?

Back

It means the system of equations has infinitely many solutions.