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 when a system of equations has one solution?

Back

It means the two lines intersect at exactly one point.

Front

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

Back

It means the two lines are parallel and never intersect.

Front

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

Back

It means the two equations represent the same line, overlapping each other.

Front

How can you solve a system of equations?

Back

You can solve it by substitution, elimination, or graphing.

Front

What is the substitution method?

Back

A method where you solve one equation for one variable and substitute that value into the other equation.

Front

What is the elimination method?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve.

Front

What is the graphical method of solving a system of equations?

Back

Plotting both equations on a graph and identifying the point(s) of intersection.

Front

If two lines intersect at (3, 1), what does that indicate about the system?

Back

It indicates that the system has one unique solution.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.