Review- Systems of Equations: ALL methods

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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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 a graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect, which represents the solution.

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

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

Back

Substitute the solution values back into the original equations to see if they hold true.

Front

What is the y-intercept of a linear equation?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the slope of a line?

Back

The rate of change of y with respect to x, calculated as rise over run (change in y/change in x).