System of equations review

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 to solve a system of equations by graphing?

Back

It involves plotting the equations on a graph and finding the point(s) where they intersect.

Front

What is substitution in the context of solving systems of equations?

Back

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

Front

What is elimination in the context of 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 does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you find the x-coordinate of the solution using substitution?

Back

Solve one equation for x and substitute that value into the other equation.

Front

How do you find the x-coordinate of the solution using elimination?

Back

Add or subtract the equations to eliminate y, then solve for x.

Front

What is the graphical representation of the solution to a system of equations?

Back

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

Front

What is the significance of the intersection point in a system of equations?

Back

It represents the values of the variables that satisfy all equations in the system.