Solve x+y+z=0 - ScanMath

Question

Solve the equation

Solve for x

Solve for y

Solve for z

x = - y - z

Evaluate

x + y + z = 0

Move the expression to the right-hand side and change its sign

x = 0 - (y + z)

Solution

More Steps

Evaluate

0 - (y + z)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

0 - y - z

Removing 0 doesn't change the value,so remove it from the expression

- y - z

x = - y - z

Show Solution

Find the partial derivative

Find \frac{\partial z}{\partial x} by differentiating the equation directly

Find \frac{\partial z}{\partial y} by differentiating the equation directly

\frac{\partial z}{\partial x} = - 1

Evaluate

x + y + z = 0

Find \frac{\partial z}{\partial x} by taking the derivative of both sides with respect to x

\frac{\partial}{\partial x} (x + y + z) = \frac{\partial}{\partial x} (0)

Use differentiation rule \frac{\partial}{\partial x} (f (x) \pm g (x)) = \frac{\partial}{\partial x} (f (x)) \pm \frac{\partial}{\partial x} (g (x))

\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (0)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

1 + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (0)

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

1 + 0 + \frac{\partial}{\partial x} (z) = \frac{\partial}{\partial x} (0)

Evaluate

1 + 0 + \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (0)

Removing 0 doesn't change the value,so remove it from the expression

1 + \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (0)

Find the partial derivative

1 + \frac{\partial z}{\partial x} = 0

Move the constant to the right-hand side and change its sign

\frac{\partial z}{\partial x} = 0 - 1

Solution

\frac{\partial z}{\partial x} = - 1

Show Solution