Systems of Equations Test Review

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 find the point(s) where the graphs of the equations intersect.

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

What are the possible types of solutions for a system of equations?

Back

One solution, no solution, or infinitely many solutions.

Front

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

Back

If the lines represented by the equations are parallel, they will 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

Solve the system by graphing: y = 2x + 1 and y = -x + 5. What is the solution?

Back

(2, 5)

Front

Solve the system by substitution: y = 3x + 1 and 2x + y = 10. What is the solution?

Back

(3, 10)

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

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

Back

Solve one of the equations for one variable.