Solving Systems of Linear Equations

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 for two lines to intersect on a graph?

Back

It means that the two equations have a common solution (x, y) that satisfies both equations.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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 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 infinitely many solutions?

Back

The lines represented by the equations overlap each other, meaning they are the same line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the graphical method of solving systems of equations?

Back

Plotting both equations on a graph and identifying the point(s) where they intersect.

Front

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

Back

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

Front

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

Back

Solve one of the equations for one variable in terms of the other variable.