Systems of Equations - Classwork 12/3

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 for a system of equations to have no solution?

Back

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

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

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 that expression is substituted into the other equation.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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

Front

How can you determine if a system of equations has one solution?

Back

If the graphs of the equations intersect at exactly one point, the system has one solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

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

Back

Graph each equation on the same coordinate plane.

Front

What does it mean to solve a system of equations by graphing?

Back

Finding the point of intersection of the graphs of the equations.