Solving Systems of Equations Using Different Methods

Consider the given system. Which variable is best eliminated first?

Answer explanation

The variable x is best eliminated first because its coefficients are already additive inverses of each other.

Recall that 4x−4x=0.

Which two equations would help you eliminate the variable y?

Answer explanation

To eliminate the variable y, both coefficients from the two equations should be additive inverses of each other.

The LCM of 4 and 9 is 36. Thus, you multiply the first equation by 9:

9(5x+4y=−30)

45x+36y=−270

Then, you multiply the second equation by 4:

4(3x−9y=−18)

12x−36y=−72

The new equations can now be added and the y variables can now be eliminated.

Consider the following system of linear equations. Which of the following is a good start when using the elimination method to solve this system?

• multiplying the second equation by 1

• multiplying the first equation by -2

• multiplying the second equation by -1

• multiplying the first equation by 2

Answer explanation

The idea behind the elimination method is to cancel one of the variables. In order for this to be possible, the coefficients of this variable need to have the same absolute value and opposite signs.

In this example, if we multiply the second equation by −1, we would then be able to add the variable x in the first equation with −x in the second one which will result to cancellation of the said variable.

Therefore, the correct answer is multiplying the second equation by −1.

Solve the following system of linear equations:

Answer explanation

Solve the following system of linear equations:

Answer explanation

Solve the following system of linear equations:

Answer explanation

Solve the given system of linear equations:

Answer explanation

What are the steps in solving for the solution to a system of linear equations in two variables using the elimination method.

Answer explanation

5 STEPS IN SOLVING SYSTEM OF LINEAR EQUATIONS BY ELIMINATION METHOD

STEP 1:

Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has the same or opposite coefficients.

STEP 2:

Add or subtract the equations to eliminate one of the variables.

STEP 3:

Solve the resulting equation.

STEP 4:

Substitute the value from Step 3 into one of the original equations and solve the other variable.

STEP 5:

Check your answer in the other equation you did not use in Step 4.

Why is it important to know different methods in solving a system of linear equations? What could possibly happen if you only know one way of solving?

Answer explanation

Knowing different methods to solve a system of linear equations allows flexibility in tackling various problems. Relying on one method may lead to difficulties with complex systems or specific cases where that method is inefficient.

Krista and Tywana were solving the system of equations below. They each shared what strategy they would use to solve the system. Who do you agree with? Is either student wrong? This is a placeholder for the diagram showing the system of equations and the strategies proposed by Krista and Tywana.

• Krista is correct, because she used the substitution method.

• Tywana is correct, because she used the elimination method.

• Both Krista and Tywana are correct, because they used two different methods.

• Neither one of them is correct.