Eliminate the x-term from the third equation

Question

2x + y − 3z = 5

2x + 3y + z = 13

6x − 4y − z = 9

Answer 1

Hey!!

When it comes to a system of 3 equations with 3 variables, you could do one of two things.

1.) Set up a matrix! This is my preferred way. You can then use row reduction/operations to get a zero in the lower left corner. If you've never seen one of these, forget I mentioned it!

2.) The algebraic way! The method of elimination is an automatic go to. The good thing is we can either choose the first and third equation, or either the second and third equation to eliminate the x. Choosing the second and third, we have:

2x+3y+z = 13

6x-4y-z = 9.

Step 2: Multiply with intention to "cancel out" x. I'm going to multiply the entire third equation by -1. And the second equation I will multiply by 3. We now have

6x + 9y + z = 13

-6x + 4y + z = -9.

When you combine these two equations (top to bottom, term by term), your x-terms will vanish!

Hope this helped!

Answer 2

We can subtract 3 times the first or second equation from the third to eliminate the x term from the third equation. Let's go with the first one:

6x - 4y - z = 9

- (6x + 3y - 9z = 15)

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-7y + 8z = -6