System 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 when 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 when a system of equations has infinite solutions?

Back

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

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 is the graphical method for solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the solution is the point of intersection.

Front

What does it mean if two lines have the same slope but different y-intercepts?

Back

The lines are parallel and will never intersect, indicating no solution for the system.

Front

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

Back

If the lines intersect at exactly one point, the system has one unique solution.

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(1, 5) - found by setting the equations equal to each other.

Front

What is the solution to the system of equations 3x + 2y = 6 and 6x + 4y = 12?

Back

Infinite solutions - the second equation is a multiple of the first.