Sometimes the elimination method is easier than the substitution method for solving systems of equations. The elimination method is so-called because the original system is replaced (if needed) by an equivalent system, where ‘addition’ of the two equations eliminates one of the variables.

Elimination has less steps than substitution. Elimination reduces the possibilities of mistakes as compared to other methods. Elimination is quicker.

The elimination method is where you actually eliminate one of the variables by adding the two equations. In this way, you eliminate one variable so you can solve for the other variable. In a two-equation system, since you have two variables, eliminating one makes the process of solving for the other quite easy.

The Elimination Method

1. Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.
2. Step 2: Subtract the second equation from the first.
3. Step 3: Solve this new equation for y.
4. Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Well for the substitution method you solve an equation for a particular variable and then substitute that equation into the other one and solve. With elimination you multiply an equation by a number and then add the two equations together and solve that way.

Substitution is best used when one (or both) of the equations is already solved for one of the variables. Elimination is best used when both equations are in standard form (Ax + By = C). Elimination is also the best method to use if all of the variables have a coefficient other than 1.

1. Step 1 : First, solve one linear equation for y in terms of x .
2. Step 2 : Then substitute that expression for y in the other linear equation.
3. Step 3 : Solve this, and you have the x -coordinate of the intersection.
4. Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.

To Solve a System of Equations by Elimination

1. Write both equations in standard form.
2. Make the coefficients of one variable opposites.
3. Add the equations resulting from Step 2 to eliminate one variable.
4. Solve for the remaining variable.
5. Substitute the solution from Step 4 into one of the original equations.