Systems of Linear Equations

Front

What are the methods to solve systems of equations?

Back

Graphing, Substitution, Elimination, All of the above.

Front

Solve the system by elimination: -4x - 4y = 0 and 4x + 4y = 0.

Back

Infinite number of solutions.

Front

Solve for x and y: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0)

Front

Does the following system have One Solution, No Solution, or Infinite Solutions? y = 4x + 8 and y = -5x + 3.

Back

One solution.

Front

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?

Back

45 minutes.

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 if a system of equations has no solution?

Back

The lines representing 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

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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.