Systems of Equations Flashcard - Graphing and 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 to graph a system of equations?

Back

To plot the equations on a coordinate plane and find the point(s) where they intersect.

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 solution to a system of equations?

Back

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

Front

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

Back

If the graphs of the equations are parallel and never intersect, the system has no 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

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

How can you check your solution to a system of equations?

Back

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

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What does the term 'slope' refer to in a linear equation?

Back

The rate at which y changes for a unit change in x, indicating the steepness of the line.