Hippocampus Algebra: Elimination method using subtraction

Let’s review the elimination method using addition.

You are given a system of equations. Use this method to find the solution.

Enter the solution into the text boxes.

Click the “Submit” button to check your answer.

Now, let’s move on with the lesson.

Here we have a system of equations:5x + 3y = 31 and 2x + 3y = 16

Notice that the coefficients of the y terms are the same. They are both 3.

Let’s subtract the second equation from the first.

We are left with only the term 3x on the left side. The y variable has been eliminated.

What is the value of x? Click the “Submit” button after entering your answer.

We find that x = 5.

Now, let’s substitute this value into one of the equations. Let’s choose the second one.

What is the value of y? Click the “Submit” button after entering your answer.

This gives us y = 2.

The ordered pair (5,2) provides the solution.

In this example system, the y coefficients were the same.

We simply subtracted one equation from the other. This eliminated the y terms.

This method is known as the elimination method using subtraction.

It can be used if the coefficients of the same variable are the same.

Here’s another system: 3y + 2x = 3 and 2x + 6y = 12. The variables are x and y.

Which variable has the same coefficients? Click the “Submit” button after selecting your answer.

The x variable has coefficients that are the same. We want to eliminate x.

What should we do next? Click the “Submit” button after selecting your answer.

Let’s subtract the first equation from the second.

This eliminates x. It also leaves the positive term 3y on the left side.

What is the value of y? Click the “Submit” button after entering your answer.

We could have subtracted the second equation from the first.

This leaves negative terms to work with. However, it gives the same y value.

Next, we substitute the y value into either equation.

This gives us x = -3.

What is the ordered pair solution of the system? Click the “Submit” button after entering your answer.

The solution is (-3,3). Let’s check it. We substitute the values into both equations.

Both equations are satisfied.

Now, try some examples on your own.

You are given a system of equations. Solve it by the elimination method using subtraction.

Enter the solution into the text boxes.

Click the “Submit” button to check your answer.

Remember: use elimination by subtraction for same coefficients. Use elimination by addition for opposite coefficients.