Question

(v) x + y + z = 3, y + 3z = 4, x – 2y + z =0​

Answer 1

Given:-

• x + y + z = 3 ---i
• y + 3z = 4 -------ii
• x - 2y + z = 0---iii

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Need to find:-

• x = ?
• y = ?
• z = ?

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Solution:-

From ii equation,

y + 3z = 4

→ y= 4 - 3z ----- A

━━━━━━━━━━━

From equation I,

x + y + z = 3

→ x + (4 - 3z) + z = 3 (From eq A, y = 4 - 3z)

→ x + 4 - 2z = 3

→ x = 3 - 4 + 2z

→ x = 2z - 1 ------ B

━━━━━━━━━━━

From iii equation,

x - 2y + z = 0

→ (2z - 1) - 2 (4 - 3z) + z = 0 (Substituting value of x and y from A and B respectively)

→ 2z - 1 - 8 + 6z + z =0

→ 9z - 9 = 0

→ 9z = 9

→ $\red{\boxed{\bold{\large{ z = 1}}}}$

━━━━━━━━━━━

Susbtitute value of z in Eq A

y = 4 - 3z

→ y = 4 - 3

→ $\red{\boxed{\bold{\large{ y= 1}}}}$

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Susbtitute value of z in Eq B

→ x = 2z - 1

→ x = 2 - 1

→ $\red{\boxed{\bold{\large{ x= 1}}}}$

Answer 2

Step-by-step explanation:

Given:-

x + y + z = 3 ---i

y + 3z = 4 -------ii

x - 2y + z = 0---iii

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Need to find:-

x = ?

y = ?

z = ?

━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀

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${\tt{\orange{\underline {\underline {\huge{Solution}}}}}}$

From ii equation,

y + 3z = 4

→ y= 4 - 3z ----- A

━━━━━━━━━━━

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

From equation I,

x + y + z = 3

→ x + (4 - 3z) + z = 3 (From eq A, y = 4 - 3z)

→ x + 4 - 2z = 3

→ x = 3 - 4 + 2z

→ x = 2z - 1 ------ B

━━━━━━━━━━━

From iii equation,

x - 2y + z = 0

→ (2z - 1) - 2 (4 - 3z) + z = 0 (Substituting value of x and y from A and B respectively)

→ 2z - 1 - 8 + 6z + z =0

→ 9z - 9 = 0

→ 9z = 9

→ $\Black{\boxed{\bold{\large{ z = 1}}}}$

z=1

━━━━━━━━━━━

Susbtitute value of z in Eq A

y = 4 - 3z

→ y = 4 - 3

→ $\red{\boxed{\bold{\large{ y= 1}}}}$

y=1

━━━━━━━━━━━

Susbtitute value of z in Eq B

→ x = 2z - 1

→ x = 2 - 1

→ ${\small{\mathcal{\red{X=1}}}}$