Solve the system of linear equations. -3x + 2y + 8z = 10 x +...

Given System of Equations
-3x + 2y + 8z = 10 (Equation 1)
x + 2y - 8z = 10 (Equation 2)
-5x - 6y - 8z = 10 (Equation 3)

Step 1: Add equations to eliminate same variable:
First, we add Equation 2 to Equation 1:
-3x + 2y + 8z + (x + 2y - 8z) = 10 + 10
-2x + 4y = 20 (Equation 4)

Then, we add Equation 3 to Equation 1:
-3x + 2y + 8z + (-5x - 6y - 8z) = 10 + 10
-8x - 4y = 20 (Equation 5)

Step 2: Combine new equations:
Now we add Equation 5 to Equation 4 to solve for x:
-2x + 4y + (-8x - 4y) = 20 + 20

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Algebra-2

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