Systems 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 a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, overlapping each other.

Front

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

Back

By plotting the equations on a graph and identifying the point of intersection.

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 elimination method 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

What is the graphical representation of the solution (1, -1)?

Back

The point where x=1 and y=-1 intersects on the graph.

Front

If two lines intersect at a point, what can be said about the system of equations?

Back

The system has one unique solution.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.