Question

If: x+y+z=2-x+3y+2z=84x+y=4Find the value of x, y and z

Answer 1

We have

$\begin{gathered} x+y+z=2 \\ -x+3y+2z=8 \\ 4x+y=4 \end{gathered}$

We have with the third equation

$y=4-4x$

We substitute in the first and second equation

$\begin{gathered} x+4-4x+z=2 \\ -3x+z=-2 \end{gathered}$$\begin{gathered} -x+3(4-4x)+2z=8 \\ -x+12-12x+2z=8 \\ -13x+2z=8-12 \\ -13x+2z=-4 \end{gathered}$

Then we have

$z=-2+3x$

We substitute

$\begin{gathered} -13x+2(-2+3x)=-4 \\ -13x-4-6x=-4 \\ -19x=0 \\ x=0 \end{gathered}$

if x=0

$z=-2$

and if x=0

$y=4$

ANSWER

x=0

y=4

z=-2