First one
Simplifying
5x + -3y + z = -6
Solving
5x + -3y + z = -6
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '3y' to each side of the equation. 5x + -3y + 3y + z = -6 + 3y
Add '3y' to each side of the equation.
5x + -3y + 3y + z = -6 + 3y
Combine like terms: -3y + 3y = 0
5x + 0 + z = -6 + 3y
5x + z = -6 + 3y
Add '-1z' to each side of the equation.
5x + z + -1z = -6 + 3y + -1z
Combine like terms: z + -1z = 0
5x + 0 = -6 + 3y + -1z
5x = -6 + 3y + -1z
Divide each side by '5'.
x = -1.2 + 0.6y + -0.2z
Simplifying
x = -1.2 + 0.6y + -0.2z
Second one
Simplifying
x + 3y + -1z = 0
Solving
x + 3y + -1z = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
x + 3y + -3y + -1z = 0 + -3y
Combine like terms: 3y + -3y = 0
x + 0 + -1z = 0 + -3y
x + -1z = 0 + -3y
Remove the zero:
x + -1z = -3y
Add 'z' to each side of the equation.
x + -1z + z = -3y + z
Combine like terms:
-1z + z = 0 x + 0 = -3y + z
x = -3y + z
Simplifying x = -3y + z
Third one
Simplifying
4x + y + z = 7
Solving
4x + y + z = 7
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1y' to each side of the equation.
4x + y + -1y + z = 7 + -1y
Combine like terms: y + -1y = 0
4x + 0 + z = 7 + -1y
4x + z = 7 + -1y
Add '-1z' to each side of the equation.
4x + z + -1z = 7 + -1y + -1z
Combine like terms: z + -1z = 0
4x + 0 = 7 + -1y + -1z
4x = 7 + -1y + -1z
Divide each side by '4'.
x = 1.75 + -0.25y + -0.25z
Simplifying
x = 1.75 + -0.25y + -0.25z
Hope all of this helps