Question

solve 3x+y-3z=1 -2x-y+2z=1 -x-y+z=2

Answer 1

Hope it's helpful to you

Answer 2

$\: 3x+y-3z=1 \\ \: \: -2x-y+2z=1 \\-x-y+z=2$

$———————————————————$

Multiply equation 3 by 3 and add it to equation 1.

$3x+y–3z=1$

$–3x–3y+3z=6$

$———————————————————$

$–2y=7$

$===>y= \frac{ - 7}{2}$

$———————————————————$

Multiply equation 3 by 2 and add it to equation 2.

$2x–y+2z=1$

$–2x–2y+2z=4$

$———————————————————$

$–3y+4z=5$

$===>4z=5+3y=5+3( \frac{ - 7}{2} )= \frac{ - 11}{2}$

$===>z= \frac{ - 11}{8}$

$———————————————————$

Now, substitute values of y and z to get x in any equation.

$–x–y+z=2$

$–x+ \frac{7}{2} – \frac{11}{8} =2$

$–x+ \frac{17}{8} =2$

$x= \frac{17}{8} –2= \frac{1}{8}$

$———————————————————$

THEREFORE,

$x = \frac{1}{8}$

$y = \frac{ - 7}{2}$

$z = \frac{ - 11}{2}$

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