Solve Systems of Linear Equations by Substitution and Elmination

Front

What is a system of linear equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

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

Back

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

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

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinite solutions.

Front

Solve by substitution: y = 2x + 1 and 3x + 2y = 12. What is the solution?

Back

(2, 5).

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

How do you determine if a system of equations is consistent?

Back

If there is at least one solution, the system is consistent.