Systems Substitution

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 infinite solutions?

Back

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

Front

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

Back

If the lines represented by the equations intersect at exactly one point, the system has one solution.

Front

What is substitution 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

Solve the system of equations: 2x + 3y = 12 and x - y = 1.

Back

(3, 2)

Front

Solve the system of equations: x + y = 5 and x - y = 1.

Back

(3, 2)

Front

What is the graphical representation of a system of equations?

Back

It is the intersection points of the lines represented by the equations on a coordinate plane.

Front

What does it mean if two equations are dependent?

Back

It means they represent the same line and have infinite solutions.

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.