- #1

Ewan_C

- 8

- 0

**[Solved] 3x4 system of equations**

## Homework Statement

Consider the following system of three equations in x, y and z.

2

*x*+ 4

*y*+ 5

*z*= 17

4

*x*+

*ay*+ 3

*z*=

*b*

8

*x*+ 7

*y*+ 13

*z*= 40

Give values for

*a*and

*b*in the second equation that make this system consistent, but with an infinite set of solutions.

## The Attempt at a Solution

I found the answers

*a*= -1,

*b*=6 easily enough. I was told by my teacher that if a system of three equations has infinite solutions, one of the equations can be found from the other two. I multiplied equation 1 by 2 and subtracted the result from equation 3. This gave:

4

*x*-

*y*+ 3

*z*= 6

and so finding the values of

*a*and

*b*was pretty simple from there. Plugging the numbers into a calculator gave an infinite number of solutions.

My question is, how can I better explain how to get

*a*and

*b*from the provided data? My method just seems like an educated guess rather than solid evidence - I don't think it'd look very good to an examiner. Cheers.

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