Systems of Equations-graphs

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 a solution?

Back

A solution is a set of values for the variables that makes all equations true.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect at a point?

Back

The system has a unique solution at that point.

Front

What does it mean if two lines are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide?

Back

The system has infinitely many solutions because the lines are the same.

Front

How do you find the solution of a system of equations graphically?

Back

By identifying the point of intersection of the graphs.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) to the run (change in x).