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 for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies all, it's a solution.

Front

What is the substitution method in solving systems of equations?

Back

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

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 graphical method for solving systems of equations?

Back

Plotting the equations on a graph and finding the intersection point.

Front

Solve the system of equations: y = 2x + 1 and y = -x + 4.

Back

(1, 3) is the solution.

Front

Solve the system of equations: 2x + 3y = 6 and x - y = 1.

Back

(3, 0) is the solution.