Solving Systems (All Methods)

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 solve a system of equations by graphing?

Back

It means to plot the equations on a graph and find the point(s) where they intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then that expression is substituted into the other equation.

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you determine the solution of a system of equations graphically?

Back

By identifying the point(s) where the graphs of the equations intersect.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

What is the purpose of rearranging equations in the substitution method?

Back

To express one variable in terms of the other, making substitution possible.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.