Solve by 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 simultaneously.

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean when a system of equations has infinite solutions?

Back

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

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

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

Back

By substituting the solution back into both original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What does the equation 4 = 7 signify in the context of systems of equations?

Back

It signifies that the system has no solution, as this statement is false.

Front

If you graph the same equation twice, what is the result?

Back

You will have infinite solutions, as both lines overlap completely.

Front

What is the solution to the system of equations 3x - y = -8 and x = -2?

Back

The solution is (-2, 2).

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19 using substitution?

Back

The solution is (2, 5).