Solve 3 x - 2 y + 3 z = 6

Question

Solve the equation

Solve for x

Solve for y

Solve for z

x = \frac{6 + 2 y - 3 z}{3}

Evaluate

3 x - 2 y + 3 z = 6

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

3 x = 6 - (- 2 y + 3 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

3 x = 6 + 2 y - 3 z

Divide both sides

\frac{3 x}{3} = \frac{6 + 2 y - 3 z}{3}

Solution

x = \frac{6 + 2 y - 3 z}{3}

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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

3 x - 2 y + 3 z = 6

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

\frac{\partial}{\partial x} (3 x - 2 y + 3 z) = \frac{\partial}{\partial x} (6)

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} (3 x) - \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (3 z) = \frac{\partial}{\partial x} (6)

Evaluate

More Steps

Evaluate

\frac{\partial}{\partial x} (3 x)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

3 \times \frac{\partial}{\partial x} (x)

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

3 \times 1

Multiply the terms

3

3 - \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (3 z) = \frac{\partial}{\partial x} (6)

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

3 - 0 + \frac{\partial}{\partial x} (3 z) = \frac{\partial}{\partial x} (6)

Evaluate

More Steps

Evaluate

\frac{\partial}{\partial x} (3 z)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

3 \times \frac{\partial}{\partial x} (z)

Find the derivative

3 \frac{\partial z}{\partial x}

3 - 0 + 3 \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (6)

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

3 + 3 \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (6)

Find the partial derivative

3 + 3 \frac{\partial z}{\partial x} = 0

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

3 \frac{\partial z}{\partial x} = 0 - 3

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

3 \frac{\partial z}{\partial x} = - 3

Divide both sides

\frac{3 \frac{\partial z}{\partial x}}{3} = \frac{- 3}{3}

Divide the numbers

\frac{\partial z}{\partial x} = \frac{- 3}{3}

Solution

More Steps

Evaluate

\frac{- 3}{3}

Reduce the numbers

\frac{- 1}{1}

Calculate

- 1

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

Show Solution