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 if two lines in a system of equations are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines in a system of equations are the same line?

Back

The system has infinitely many solutions because every point on the line is a solution.

Front

What is substitution 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 elimination 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.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean for a system of equations to be consistent?

Back

The system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

The system has no solutions.