Substitution and Elimination Methods (ALG I)

The elimination method involves adding or subtracting equations to eliminate one variable, making it possible to solve for the other variable.

To set up equations for elimination, align the equations so that corresponding variables and constants are in the same columns, and manipulate the equations to have coefficients that can be easily eliminated.

The first step is to manipulate the equations, if necessary, to make the coefficients of one of the variables the same or opposites.

After eliminating one variable, solve the resulting single-variable equation for the remaining variable.

Substitute the value of the solved variable back into one of the original equations to find the value of the other variable.

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

The elimination method is often more advantageous when the coefficients of the variables are easily manipulated to eliminate one variable.

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

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

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