Plug and Chug: Systems of Equations

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 point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation and check if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations, where the intersection point(s) represent the solution(s).

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 is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution, as the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

It means there are infinitely many solutions, as the lines are the same.

Front

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

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

How can you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if both are satisfied.