Solving Systems with Graphing and Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

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

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the first step in using the substitution method?

Back

Isolate one variable in one of the equations.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

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 both equations are satisfied.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at exactly one point.

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never intersect.