SOLUTION: I DONT UNDERSTAND THIS PLEASE HELP..! Use Cramer’s rule to solve for y in the following system of equations. x + 4y – 2z = 3 x + 3y + 7z = 1 2x + 9y + z = 8

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Question 433873: I DONT UNDERSTAND THIS PLEASE HELP..!
Use Cramer’s rule to solve for y in the following system of equations.
x + 4y – 2z = 3
x + 3y + 7z = 1
2x + 9y + z = 8

Answer by tlwright(1)   (Show Source): You can put this solution on YOUR website!
Solve using Cramer's Rule:

x + 4y – 2z = 3
x + 3y + 7z = 1
2x + 9y + z = 8
Step 1, calculate the denominator Delta (Δ):
Δ = (1 * 3 * 1) + (4 * 7 * 2) + (-2 * 1 * 9) - (-2 * 3 * 2) - (1 * 7 * 9) - (4 * 1 * 1)
Δ = 3 + 56 - 18 + 12 - 63 - 4
Δ = -14
Step 2, calculate the x numerator:
x numerator = (3 * 3 * 1) + (4 * 7 * 8) + (-2 * 1 * 9) - (-2 * 3 * 8) - (3 * 7 * 9) - (4 * 1 * 1)
x numerator = 9 + 224 - 18 + 48 - 189 - 4
x numerator = 70
Step 3, calculate the y numerator:
y numerator = (1 * 1 * 1) + (3 * 7 * 2) + (-2 * 1 * 8) - (-2 * 1 * 2) - (1 * 7 * 8) - (3 * 1 * 1)
y numerator = 1 + 42 - 16 + 4 - 56 - 3
y numerator = -28
Step 4, calculate the z numerator:
(1 * 3 * 8) + (4 * 1 * 2) + (3 * 1 * 9) - (3 * 3 * 2) - (1 * 1 * 9) - (4 * 1 * 8)
z numerator = 24 + 8 + 27 - 18 - 9 - 32
z numerator = 0
Calculate X
x = x numerator
Δ
x = 70
-14
X = -5
Calculate Y
y = y numerator
Δ
y = -28
-14
Y = 2
Calculate Z
z = z numerator
Δ
z = 0
-14
Z = 0
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