Solving Systems of Linear Equations

Front

What are the three methods to solve systems of linear equations?

Back

Graphing, substitution, and elimination.

Front

What is the solution to the system of equations represented by the point (1, -1)?

Back

(1, -1) is the solution.

Front

If a younger brother spent $175 on 7 shirts and 7 shorts, and an older brother spent $165 on 6 shirts and 7 shorts, how much does one shirt cost?

Back

One shirt costs $10.

Front

What does it mean if a system of equations has 0 solutions?

Back

It means the lines are parallel and never intersect.

Front

What is the next step in substitution if you have the equation 3x - 7(-2y-21) = 41?

Back

3(-2y-21) - 7y = 41.

Front

Define a system of linear equations.

Back

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

Front

What does it mean for a system to have infinitely many solutions?

Back

It means the equations represent the same line.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution; an inconsistent system has no solutions.

Front

What is the substitution method in solving systems of equations?

Back

Replacing one variable with an expression from another equation.