System of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

What is the method of substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.

Front

What does it mean for two lines to intersect?

Back

They meet at a point, which is the solution to the system of equations.

Front

How many solutions does a system of equations with intersecting lines have?

Back

One solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by lines on a coordinate plane.

Front

What is the significance of the slopes of lines in a system of equations?

Back

If the slopes are the same, the lines are parallel and have no solutions.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.