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 no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How can you determine the number of solutions in a system of 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 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, making it easier to solve.

Front

What is the graphical method for solving systems of equations?

Back

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

Front

Solve the system of equations: y = 2x + 3 and y = -x + 1. What is the solution?

Back

(−2, −1)

Front

Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the solution?

Back

(3, 0)