Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to intersect?

Back

It means that the two lines have a common solution, which is the point where they meet.

Front

How can 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 does it mean if a system of equations has no solution?

Back

It means the lines are parallel and will never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

Solve for x and y: 3x - 3y = 33 and 6x - 3y = 57.

Back

(8, -3)

Front

What is the solution to the system: y = 5x and 3x + y = 24?

Back

(3, 15)

Front

Solve for x and y: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0)