Systems of Equations - Cumulative

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 a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

When would you add equations in the elimination method?

Back

You would add equations when the coefficients of one variable are opposites, allowing for elimination.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

How can you check the solution of a system of equations?

Back

By substituting the solution back into the original equations to see if they hold true.

Front

What is the graphical method of solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What does it mean if two lines intersect at one point?

Back

It means the system has a unique solution, which is the coordinates of the intersection point.

Front

What is the significance of the point (3, -3) in a system of equations?

Back

It is a potential solution that can be verified by substituting into the original equations.