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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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

How do you graphically solve a system of equations?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the solution to a system of equations?

Back

The point(s) (x, y) where the equations intersect, representing the values of the variables that satisfy all equations.

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 equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

(3, 0)

Front

Solve using substitution: 5x - 4y = -16 and x + 2y = -6.

Back

(-4, -1)