# Solving Systems of Equations by Elimination 03:36 minutes

**Video Transcript**

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Transcript
**Solving Systems of Equations by Elimination**

Far, far away, in a distant universe, in the **System of Equations**, on a previously unexplored planet called **Elimination**, a brave, but mathematically-challenged shuttle crew has been tasked with bringing home samples from the planet.

The crew has twenty-five containers to collect samples of material A and material B. They have determined that a container filled with sample A has a mass of three tons, and a container filled with sample B has a mass of seven tons.

In order to return to Earth safely, the filled containers must not have a total mass of more than one hundred fifteen tons. How many containers of each sample can be transported on the space shuttle? Let's help the crew figure out this problem!

### Translating a Word Problem into a System of Equations

Since an error in the **calculation** could mean a major disaster for the space travelers, let’s go over the information one more time.

- There are 25 containers.
- Each container of sample A weighs 3 tons.
- And each container of sample B weighs 7 tons.
- The total allowed is 115 tons.

To describe this situation, we can write two equations then use a **system of equations** to solve for the two unknowns: x, the number of containers of sample A, and y, the number of containers of sample B.

Let's write it on the board, x + y = 25, and 3x + 7y = 115. Notice how we've line up the variables.

### Eliminating Variables

Now let’s **manipulate one or both of the equations** as needed. We can use **addition or subtraction** to **eliminate one of the variables**.

Hmm, how can we eliminate one of the variables? How about we multiply the first equation, x + y = 25, by negative three? We distribute −3 to each term.

Now we can add our two equations. We see that −3x + 3x cancels out to 0x, which is 0, −3y + 7y = 4y, and −75 + 115 = 40… See how the variable x is eliminated?

### Solving a System of Equations for the Unknowns

Now, solve for y. We can **divide both sides** by 4 and see that y is equal to 10. Next, substitute 'y = 10' into one of the original equations, so you can solve for x.

We can use either of the original equations and our answer will be the same; let's save time and pick the least complicated equation.

- When we plug in 10 for y, we have x + 10 = 25.
- Subtract 10 from both sides: x = 15.

The crew learns they can take 15 containers of sample A and 10 containers of sample B. Whew-hoo! Crisis averted!

Hold on! What’s happening? They can’t start ! There's a stowaway! (No problem, they can activate a specially designed wiper, designed especially for an emergency such as this. Watch how that stowaway will be wiped away!)

**All Video Lessons & Practice Problems in Topic**Systems of Equations and Inequalities »