After Multiplying 3 with the eq. (i) we will add this to eq. (ii)
[tex] \sf 18x - 6y + 3z = - 2[/tex]
[tex] \sf2x + 3y - 3z = 11[/tex]
[tex]⇒ \sf20x - 3y = 9 \: \: .........(iv)[/tex]
After Multiplying 2 with the eq. (iv) we will add this to eq. (iii)
[tex] \sf \: x + 6y = 31[/tex]
[tex] \sf40x - 6y = 18[/tex]
[tex] \sf \: 41x = 49[/tex]
[tex]⇒ \sf \: x = \frac{49}{41} [/tex]
After putting the value of x in the eq. (iii)
[tex] \sf \frac{49}{41} + 6y = 31[/tex]
[tex]⇒ \sf6y = 31 - \frac{49}{41} [/tex]
[tex] \sf \: ⇒ 6y = \frac{1271 - 49 }{41} [/tex]
[tex]⇒ \sf6y = \frac{1222}{41} [/tex]
[tex]⇒ \sf \: y = \frac{1222}{41 \times 6} [/tex]
[tex]⇒ \sf \: y = \frac{611}{123} [/tex]
After putting the value of x and y into eq. (i)
[tex] \sf6 \times \frac{49}{41} - 2 \times \frac{611}{123} + z = -2 [/tex]
[tex]⇒ \sf\frac{294}{41} - \frac{1222}{123} + 2 = - z[/tex]
[tex]⇒ \sf \frac{882 - 1222 + 246}{123} = - z[/tex]
[tex]⇒ \sf - \frac{94}{123} = - z[/tex]
[tex]⇒ \sf \: z = \frac{94}{123} [/tex]
Hence,
[tex] \bf • \: The \: value \: of \: x = \frac{49}{41}
[tex] \bf • \: The \: value \: of \: x = \frac{49}{41} [/tex]
[tex] \bf • \: The \: value \: of \: y = \frac{611}{123}
[tex] \bf • \: The \: value \: of \: y = \frac{611}{123}[/tex]
[tex] \bf• \: The \: value \: of \: z \: = \frac{94}{123}[/tex]
