Systems of Equations (Graphing and Substitution)

Front

What is a system of equations?

Back

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

Front

What does it mean to graph a system of equations?

Back

To plot the equations on a coordinate plane and find their intersection point(s).

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

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

How do you determine if a system has no solution?

Back

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

Front

What does it mean if a system 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 the system: y = 2x + 1 and y = 4x - 1?

Back

Set the equations equal to each other: 2x + 1 = 4x - 1, solve for x, then substitute back to find y.

Front

What is the graphical representation of the solution (6, -2)?

Back

It is the point where the two lines intersect on the graph.

Front

What does it mean if two equations are dependent?

Back

They represent the same line and have infinitely many solutions.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.