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 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 graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is the solution to the system of equations: x + 2y = -4 and x - 2y = 8?

Back

(2, -3)

Front

What is elimination in the context of solving systems of equations?

Back

A method to eliminate one variable by adding or subtracting equations.

Front

What must the coefficients of the eliminated variable be in elimination?

Back

The same number opposite signs (opposites).

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 infinite solutions?

Back

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

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.

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.