Solution to system of linear equations

Question

What is the solution of the system of linear equations

8x + 3y + 6z = 7

3x + 1y + 8z = 4

Answer 1

If you REALLY only have 2 equations with 3 unknowns, then you pick one variable and then solve for the others in terms of that variable.

For example, I'll pick "z" as the variable to keep. So multiply the bottom equation by -3 giving:

-9x - 3y - 24z = -12

Then add this to the 1st equation:

-9x - 3y - 24z = -12

8x + 3y + 6z = 7

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-x - 18z = -5

-x = 18z - 5

x = -18z + 5

Now, multiply the 1st equation by -3 and the second equation by 8 then add them to get:

-24x - 9y - 18z = -21

24x+ 8y + 64z = 32

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-y + 46z = 11

So y = 46z - 11

So:

z = z

y = 46z - 11

x = -18z + 5

Obviously, you would have different answers depending on which variable you chose to keep.