Solve ∫ 2k/3-5y/4=-3

$$\int \frac { 2 k } { 3 } - \frac { 5 y } { 4 } = - 3$$

Solve for y

$$y=\frac{8kx+С}{15}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4\int \frac{2k}{3}\mathrm{d}x-5y=-12$$

Subtract 4\int \frac{2k}{3}\mathrm{d}x from both sides.

$$-5y=-12-4\int \frac{2k}{3}\mathrm{d}x$$

The equation is in standard form.

$$-5y=-\frac{8kx}{3}-4С-12$$

Divide both sides by -5.

$$\frac{-5y}{-5}=\frac{-\frac{8kx}{3}-4С-12}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$y=\frac{-\frac{8kx}{3}-4С-12}{-5}$$

Divide -12-\frac{8kx}{3}-4С by -5.

$$y=\frac{8kx}{15}+\frac{4С}{5}+\frac{12}{5}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{15y-С}{8x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=\frac{4С}{5}\text{ and }x=0\end{matrix}\right.$$