Solving System 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 to solve a system of equations?

Back

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

Front

What are the three main methods for solving systems of equations?

Back

1. Graphing 2. Substitution 3. Elimination

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method that involves adding or subtracting equations 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

The lines represented by 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

How do you determine 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

Solve the system: x + y = 5 and x - y = 1.

Back

(3, 2) is the solution.

Front

Solve the system: 2x + 3y = 6 and 4x - y = 5.

Back

(2, 0) is the solution.