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 be parallel in a system of equations?

Back

They have the same slope and will never intersect.

Front

How can you solve a system of equations using substitution?

Back

By solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the lines representing the equations intersect.

Front

What is an ordered pair in the context of systems of equations?

Back

A pair of numbers (x, y) that represents a point on the Cartesian plane.

Front

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

Back

The lines are parallel and do not intersect.

Front

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

Back

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

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an expression derived from another 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 is the significance of the slopes of two lines in a system of equations?

Back

The slopes determine whether the lines are parallel, intersecting, or coincident.