Solve the system of linear equations. x + 4y - 6z = -1 2x - ...

Given System of Equations
x + 4y - 6z = -1 (Equation 1)
2x - y + 2z = -7 (Equation 2)
-x + 2y - 4z = 5 (Equation 3)

Step 1: Multiply Equation 2 by 2
First, we multiply Equation 2 by 2 to facilitate the elimination of (y and z):
2(2x - y + 2z) = 2(-7)
4x - 2y + 4z = -14 (Equation 4)

Step 2: Add Equation 4 to Equation 3
Now we add Equation 4 to Equation 3 to eliminate (y and z):
-x + 2y - 4z + (4x - 2y + 4z) = 5 + (-14)
3x = -9
x = -3

Step 3: Substitute x = -3 into Equation 2
Next, we substitute x into Equation 2 to express y in terms of z:
2(-3) - y + 2z = -7
-6 -...

Algebra-2

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