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 lines representing the equations intersect at exactly one point.

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 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 graphs of the equations or using algebraic methods like substitution or elimination.

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

Back

(1, 3) - The point where the two lines intersect.

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 does it mean for two equations to be dependent?

Back

They represent the same line and have infinitely many solutions.