System of Equations Review

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 two lines to be parallel in a system of equations?

Back

Parallel lines have the same slope but different y-intercepts, resulting in no solutions.

Front

What is the solution of a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What is the significance of the slopes of lines in a system of equations?

Back

If the slopes are the same and the y-intercepts are different, the system has no solutions. If the slopes are different, the system has one solution.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel (same slope, different y-intercepts), the system has no 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

Back

(1, 2) is the 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 does it mean for a system of equations to have one solution?

Back

The lines intersect at exactly one point, which is the unique solution to the system.