Elimination Method: Systems of Equations

The elimination method is a technique used to solve systems of equations by eliminating one variable, allowing for the other variable to be solved directly.

To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing them to cancel out when the equations are added or subtracted.

(3, 0)

A system of equations has no solution if the lines represented by the equations are parallel, meaning they never intersect.

(1, 2.5)

A consistent system of equations is one that has at least one solution, meaning the lines intersect at one or more points.

Infinitely many solutions (the second equation is a multiple of the first).

An inconsistent system of equations is one that has no solutions, typically because the equations represent parallel lines.

Infinitely many solutions (the second equation is a multiple of the first).

The first step is to align the equations and decide which variable to eliminate.