Algebra 2 Section 3.1 Solving Systems Using Tables and Graphs

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 for a system of equations to be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Front

What are dependent equations?

Back

Dependent equations are equations that represent the same line, resulting in infinitely many solutions.

Front

What are independent equations?

Back

Independent equations are equations that represent different lines, resulting in exactly one solution.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

Front

How can you determine if a solution is valid for a system of equations?

Back

Plug the solution back into each equation to see if it satisfies all equations in the system.

Front

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

Back

(1, 3) is the solution.

Front

What does it mean for two lines to intersect at a point?

Back

It means that the system of equations has one unique solution.