Solving 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 no solution?

Back

It means the lines represented by the equations 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, so every point on the line is a solution.

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they 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 is the point of intersection in a system of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

Solve for x and y: y = 2x + 1 and y = 4x - 1

Back

(1, 3)

Front

Solve for x and y: 2x - 3y = -1 and y = x - 1

Back

(4, 3)

Front

What is the graphical representation of the solution (3, 1)?

Back

It is the point where the two lines intersect on a graph.