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Solving systems of Equations

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Please help with the following problems. Provide step by step calculations.

3. Solve for X, Y, and Z in the following systems of three equations:

a. X + 2Y + Z = 6
X + Y = 4
3X + Y + Z = 8

b. 10X + Y + Z = 12
8X + 2Y +Z = 11
20X - 10Y - 2Z = 8

c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z = 5
9X + 2Y + 12Z = 14

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This solution shows how to solve systems of equations in three variables. Step by step calculations are given for each problem.

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3. Solve for X, Y, and Z in the following systems of three equations:

a. X + 2Y + Z = 6 --------------(i)
X + Y = 4 -------------------(ii)
3X + Y + Z = 8 ------------(iii)

Solution:

Subtract equation (ii) from (i), we will get
Y + Z = 2-----------------(iv)

Multiply equation (ii) by 3
3X + 3Y = 12

Now, subtract it from equation (iii), we will get

-2Y + Z = -4------------(v)

Subtract equation (v) from (iv), we will get

3Y = 6
Y = 2

Now from ...

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