Solve Systems of Equations by Elimination

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the solution to a system of equations?

Back

The solution is the ordered pair (x, y) that satisfies all equations in the system.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What is the elimination method?

Back

The elimination method is a technique for solving systems of equations by removing one variable, allowing for easier solving of the remaining variable.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and decide whether to add or subtract them to eliminate one variable.

Front

How do you eliminate a variable?

Back

You can eliminate a variable by adding or subtracting the equations in such a way that one variable cancels out.

Front

What happens if the equations are dependent?

Back

If the equations are dependent, they represent the same line, and there are infinitely many solutions.

Front

What happens if the equations are inconsistent?

Back

If the equations are inconsistent, they represent parallel lines and have no solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.