Systems (graphing & substitution)

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 if two lines are parallel in a system of equations?

Back

It means there is no solution to the system because the lines never intersect.

Front

What does it mean if two lines are coincident in a system of equations?

Back

It means there are infinitely many solutions because the lines lie on top of each other.

Front

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

Back

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

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 is the graphing method in solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point of intersection is the solution.

Front

What is an ordered pair?

Back

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

Front

How do you check if an ordered pair is a solution to a system of equations?

Back

Substitute the x and y values of the ordered pair into both equations to see if they hold true.

Front

What is a solution to a system of inequalities?

Back

A set of values that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point on the graph.