# For systems with infinitely many solutions, write the solution set using an arbitrary variable.2x+3y+4z=3

Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramers
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$x=\frac{Dx}{D},y=\frac{Dy}{D},z=\frac{Dz}{D}$
D=|2 3 4|
|-4 2 -6| = -56
|4 6 3|
Dx=|3 3 4| / Dy=|2 3 4|
|2 2 -6| / |-4 2 -6|
|0 0 3|=0 / |4 0 3|=-56
Dz=|2 3 3|
|-4 2 2| = 0
|4 0 0|
Putting values $\to x=\frac{0}{-56}=0$
$y=\frac{-56}{-56}=1,z=\frac{0}{-56}=0$