Question

5x-4y-6z = -3
X-3y+z=-1
-3x-6y+7z=1

Answer 1

Answer:

$x=-\frac{41}{55},y=\frac{2}{55},z=-\frac{8}{55}$

Step-by-step explanation:

$5x-4y-6z=-3...............eq(1)\\\\x-3y+z=-1.....................eq(2)\\\\-3x-6y+7z=1.................eq(3)$

$eq(1)-5\times eq(2)$

$5x-4y-6z-5(x-3y+z)=-3-5\times (-1)\\\\11y-11z=2\\\\y-z=\frac{2}{11}...................eq(4)$

$3\times eq(2)+eq(3)$

$3(x-3y+z)-3x-6y+7z=3\times (-1)+1\\\\-15y+10z=-2\\\\-y+\frac{2}{3}z=-\frac{2}{15}.........eq(5)$

$eq(4)+eq(5)$

$y-z-y+\frac{2}{3}z=\frac{2}{11}-\frac{2}{15}\\\\-\frac{1}{3}z=\frac{8}{165}\\\\z=-\frac{8\times 3}{165}\\\\z=-\frac{8}{55}$

From $eq(4)$

$y=z+\frac{2}{11}=-\frac{8}{55}+\frac{2}{11}\\\\y=\frac{2}{55}$

Substitute the value of $y$ and $z$ in $eq(2)$

$x-3\times \frac{2}{55}-\frac{8}{55}=-1\\\\x-\frac{14}{55}=-1\\\\x=-1+\frac{14}{55}\\\\x=\frac{41}{55}$