Solve -0.65x+0.96y=0.45x+(z*y)

$$-0.65x+0.96y=0.45x+(z \times y)$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{55x}{2\left(24-25z\right)}\text{, }&z\neq \frac{24}{25}\\y\in \mathrm{C}\text{, }&x=0\text{ and }z=\frac{24}{25}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract zy from both sides.

$$-0.65x+0.96y-zy=0.45x$$

Add 0.65x to both sides.

$$0.96y-zy=0.45x+0.65x$$

Combine 0.45x and 0.65x to get 1.1x.

$$0.96y-zy=1.1x$$

Combine all terms containing y.

$$\left(0.96-z\right)y=1.1x$$

The equation is in standard form.

$$\left(\frac{24}{25}-z\right)y=\frac{11x}{10}$$

Divide both sides by \frac{24}{25}-z.

$$\frac{\left(\frac{24}{25}-z\right)y}{\frac{24}{25}-z}=\frac{11x}{10\left(\frac{24}{25}-z\right)}$$

Dividing by \frac{24}{25}-z undoes the multiplication by \frac{24}{25}-z.

$$y=\frac{11x}{10\left(\frac{24}{25}-z\right)}$$

Divide \frac{11x}{10} by \frac{24}{25}-z.

$$y=\frac{55x}{2\left(24-25z\right)}$$

Solve for x

$$x=\frac{2y\left(24-25z\right)}{55}$$

Steps for Solving Linear Equation

Subtract 0.45x from both sides.

$$-0.65x+0.96y-0.45x=zy$$

Combine -0.65x and -0.45x to get -1.1x.

$$-1.1x+0.96y=zy$$

Subtract 0.96y from both sides.

$$-1.1x=zy-0.96y$$

The equation is in standard form.

$$-1.1x=yz-\frac{24y}{25}$$

Divide both sides of the equation by -1.1, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-1.1x}{-1.1}=\frac{y\left(z-0.96\right)}{-1.1}$$

Dividing by -1.1 undoes the multiplication by -1.1.

$$x=\frac{y\left(z-0.96\right)}{-1.1}$$

Divide y\left(-0.96+z\right) by -1.1 by multiplying y\left(-0.96+z\right) by the reciprocal of -1.1.

$$x=-\frac{10y\left(z-0.96\right)}{11}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{55x}{2\left(24-25z\right)}\text{, }&z\neq \frac{24}{25}\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=\frac{24}{25}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract zy from both sides.

$$-0.65x+0.96y-zy=0.45x$$

Add 0.65x to both sides.

$$0.96y-zy=0.45x+0.65x$$

Combine 0.45x and 0.65x to get 1.1x.

$$0.96y-zy=1.1x$$

Combine all terms containing y.

$$\left(0.96-z\right)y=1.1x$$

The equation is in standard form.

$$\left(\frac{24}{25}-z\right)y=\frac{11x}{10}$$

Divide both sides by \frac{24}{25}-z.

$$\frac{\left(\frac{24}{25}-z\right)y}{\frac{24}{25}-z}=\frac{11x}{10\left(\frac{24}{25}-z\right)}$$

Dividing by \frac{24}{25}-z undoes the multiplication by \frac{24}{25}-z.

$$y=\frac{11x}{10\left(\frac{24}{25}-z\right)}$$

Divide \frac{11x}{10} by \frac{24}{25}-z.

$$y=\frac{55x}{2\left(24-25z\right)}$$