Solving 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 system of equations to have a unique solution?

Back

It means the lines intersect at exactly one point, representing one set of values for the variables.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect, indicating no set of values satisfies both equations.

Front

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

Back

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

Front

How do you graph a system of equations?

Back

Plot each equation on the same coordinate plane and look for points of intersection.

Front

What is the substitution method for 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 for 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 interpretation of the solution to a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

What is the slope-intercept form of a linear equation?

Back

The form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts, they are parallel.