SOLUTION: Consider the following system of equations 1. 4x+3y+3z=-8 2. 2x+y+z=-4 3. 3x-2y+(m^2-6)z=m-4 Determine the value(s) of m for which this system of equations will have: a.

Question 775466: Consider the following system of equations
1. 4x+3y+3z=-8
2. 2x+y+z=-4
3. 3x-2y+(m^2-6)z=m-4
Determine the value(s) of m for which this system of equations will have:
a. no solution
b. one solution
c. an infinite number of solution
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
1.
2.
3.
__________________
1.
2. ...multiply by 2
____________
1.
2. ......and subtract from 1.
___________________

.......solve for y
........go to 2. .substitute y

.......first solution
go to 3.,substitute x and y solve for z

=> since
so, solution will exist for all real numbers m except
if => =>........there will be no solutions
if => and
or
if => and
so, real integer solutions are:
, , for
and
, , for
and
, , for
and so on......your answer is:
c. an infinite number of solution

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