Question

If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable z is eliminated in the first and second equations, then the second and third equations.

3x – 5y + 2z = 7
4x + 9y – z = 2
x – 3y + 3z = 7

Answer 1

Nobody like triple variables

Answer 2

I love triple variables

Answer 3

first, I would move the z terms so they are the first ones (because that's how I roll)

Answer 4

then I would use Gaussian elimination

Answer 5

3x – 5y + 2z = 7 [1]
8x + 18y – 2z = 4 [2] *2
===========
11x+13y =11 [1]'

12x + 27y – 3z = 2 [1]*3
x – 3y + 3z = 7 [3]
============
13x+24y =9 [3]'

The 2x2 system would be:
11x+13y =11 [1]'
13x+24y =9 [3]'

Let's hope I didn't make an arith. error!

Answer 6

where I have [1]*3 that is supposed to read [2]*3

Answer 7

z + 1/3x -y = 7/3
x + (24/13)y = 1
y = 0

Answer 8

y = 0, x = 1, z = 2

Answer 9

I did have an error--in my second linear combination. these problems are not best solved on the computer!

12x + 27y – 3z = 6 [2]*3
x – 3y + 3z = 7 [3]
============
13x+24y =13 [3]'

The 2x2 system would be:
11x+13y =11 [1]'
13x+24y =13 [3]'

Answer 10

this seems to be ok b/c it checks with agd...o's answers