5.2 System of Equation - Elimination Method

The elimination method is a method for solving a system of equations by adding or subtracting the equations so that one of the variables is eliminated. The steps involved in the elimination method are as follows:

1. Write the equations in standard form: Both equations should be written in standard form, with the variables on the left-hand side of the equation and the constants on the right-hand side.

2. Make the coefficients of one of the variables opposites: Multiply one or both of the equations by a constant so that the coefficients of one of the variables are opposites.

3. Add or subtract the equations: Add or subtract the equations so that one of the variables is eliminated.

4. Solve for the remaining variable: Solve the resulting equation for the remaining variable.

5. Substitute the value you found in step 4 into either of the original equations to find the value of the other variable.

Here is an example of how to solve a system of equations using the elimination method:

Equation 1: 2x + 3y = 12

Equation 2: x - y = 4

First, we need to make the coefficients of y opposites. We can do this by multiplying Equation 1 by 1 and Equation 2 by 3:

Equation 1: 2x + 3y = 12

Equation 2: 3x - 3y = 12

Now, we can add the equations together:

5x = 24

x = 4

Now that we know the value of x, we can substitute it into either of the original equations to find the value of y. Let's substitute it into Equation 1:

2(4) + 3y = 12

8 + 3y = 12

3y = 4

y = 1.33

Therefore, the solution to the system of equations is x = 4 and y = 1.33.

Here are some additional tips for using the elimination method:

• If the coefficients of one of the variables are already opposites, you can add or subtract the equations directly to eliminate the variable.

• If the system of equations has no solution, the elimination method will not work. In this case, you can try using the substitution method or the graphical method to solve the system.