Solve the system of linear equations. 4x + 2y + 3z = 12 2x -...

Given System of Equations
4x + 2y + 3z = 12 (Equation 1)
2x - 3y + 5z = -7 (Equation 2)
6x - y + 4z = -3 (Equation 3)

Step 1: Multiply Equation 2 by 2
First, we multiply Equation 2 by 2 to facilitate the elimination of (x):
2(2x - 3y + 5z) = 2(-7)
4x - 6y + 10z = -14 (Equation 4)

Step 2: Subtract Equation 4 from Equation 1
Now we subtract Equation 4 from Equation 1 to eliminate (x):
4x + 2y + 3z - (4x - 6y + 10z) = 12 - (-14)
2y - (-6y) + 3z - (10z) = 12 + 14
8y - 7z = 26 (Equation 5)

Step 3: Multiply Equation 2 by 3
Next, we multiply Equation 2 by 3 to facilitate the elimination of (x):
3(2x - 3y + 5z) = 3(-7)
6x - 9y + 15z = -21 (Equation 6)

Step 4: Subtract Equation 6 from Equation 3
Now we subtract Equation 6 from Equation 3 to eliminate (x):
6x - y + 4z - (6x - 9y + ...

Algebra-2

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