Raymond B. answered • 12/03/20
Math, microeconomics or criminal justice
multiply the first equation by 2 and then add the 2nd equation
4x-6y +2z =-16
-4x+9y =15
3y +2z =-1
multiply the 1st equation by 3
6x-9y+3z = -24 add the 2nd equation
-4x+9y =15 to get
2x +3z =-9
multiply that last equation by 2 and multiply 3y+2z=-1 by 3 then subtract
4x+6z =-18
9y +6z =-3
4x-y =-15
that gives you 3 equations
4x-y=-15
2x+3z =-9
3y+2z=-1
that's the best solution you can get, relating x and y, x and z, y and z
this may look like 3 equations 3 unknowns, but they are not linearly independent.
You started with 2 equations 3 unknowns which has an infinite number of solutions
all 3 variables can take on any real value. Pick a value for any one, and you can
calculate the value of the other two.
