Solve x^3+y+2z=42x+1/5y

$$x ^ { 3 } + y + 2 z = 42 x + \frac { 1 } { 5 } y$$

Solve for y

$$y=-\frac{5x^{3}}{4}+\frac{105x}{2}-\frac{5z}{2}$$

Steps for Solving Linear Equation

Subtract \frac{1}{5}y from both sides.

$$x^{3}+y+2z-\frac{1}{5}y=42x$$

Combine y and -\frac{1}{5}y to get \frac{4}{5}y.

$$x^{3}+\frac{4}{5}y+2z=42x$$

Subtract x^{3} from both sides.

$$\frac{4}{5}y+2z=42x-x^{3}$$

Subtract 2z from both sides.

$$\frac{4}{5}y=42x-x^{3}-2z$$

The equation is in standard form.

$$\frac{4}{5}y=-x^{3}+42x-2z$$

Divide both sides of the equation by \frac{4}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{5}y}{\frac{4}{5}}=\frac{-x^{3}+42x-2z}{\frac{4}{5}}$$

Dividing by \frac{4}{5} undoes the multiplication by \frac{4}{5}.

$$y=\frac{-x^{3}+42x-2z}{\frac{4}{5}}$$

Divide 42x-x^{3}-2z by \frac{4}{5} by multiplying 42x-x^{3}-2z by the reciprocal of \frac{4}{5}.

$$y=-\frac{5x^{3}}{4}+\frac{105x}{2}-\frac{5z}{2}$$