Question

Solve the system.



6x - 2y + z = -2
2x + 3y – 3z = 11
х+ 6у = 31

Answer 1

• 6x - 2y + z = -2 .......... (i)
• 2x + 3y – 3z = 11 ...........(ii)
• х + 6у = 31 ..............(iii)

After Multiplying 3 with the eq. (i) we will add this to eq. (ii)

`\sf 18x - 6y + 3z = - 2`

`\sf2x + 3y - 3z = 11`

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`⇒ \sf20x - 3y = 9 \: \: .........(iv)`

After Multiplying 2 with the eq. (iv) we will add this to eq. (iii)

`\sf \: x + 6y = 31`

`\sf40x - 6y = 18`

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`\sf \: 41x = 49`

`⇒ \sf \: x = (49)/(41)`

After putting the value of x in the eq. (iii)

`\sf (49)/(41) + 6y = 31`

`⇒ \sf6y = 31 - (49)/(41)`

`\sf \: ⇒ 6y = (1271 - 49 )/(41)`

`⇒ \sf6y = (1222)/(41)`

`⇒ \sf \: y = (1222)/(41 * 6)`

`⇒ \sf \: y = (611)/(123)`

After putting the value of x and y into eq. (i)

`\sf6 * (49)/(41) - 2 * (611)/(123) + z = -2`

`⇒ \sf(294)/(41) - (1222)/(123) + 2 = - z`

`⇒ \sf (882 - 1222 + 246)/(123) = - z`

`⇒ \sf - (94)/(123) = - z`

`⇒ \sf \: z = (94)/(123)`

Hence,

`\bf • \: The \: value \: of \: x = (49)/(41) </strong></p><p><strong>[tex] \bf • \: The \: value \: of \: x = (49)/(41)`

`\bf • \: The \: value \: of \: y = (611)/(123)</strong></p><p><strong>[tex] \bf • \: The \: value \: of \: y = (611)/(123)`

`\bf• \: The \: value \: of \: z \: = (94)/(123)`