Solve Systems by Graphing and Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by graphing?

Back

It means to plot the equations on a graph and find the point(s) where they intersect.

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

What is substitution in the context of 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

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

Back

If the lines are parallel and never intersect, the system has no solution.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

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

Front

What is the graphical representation of the solution (1, -1)?

Back

It is the point where x=1 and y=-1 on the Cartesian plane.

Front

What does the equation 4x + 7y = 3365 represent in a word problem?

Back

It represents a relationship between two variables, often derived from a real-world scenario.

Front

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

Back

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

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.