Solving Linear Systems by Elimination

A linear system is a collection of two or more linear equations involving the same variables.

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

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

To eliminate a variable, you can multiply one or both equations by a number so that when you add or subtract the equations, one variable cancels out.

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

(2,0) - Solution found by elimination.

A consistent system has at least one solution, meaning the lines represented by the equations intersect at one or more points.

An inconsistent system has no solutions, meaning the lines represented by the equations are parallel and never intersect.

A dependent system has infinitely many solutions, meaning the equations represent the same line.

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