Solve y:15x+4yquad3x-y=11

$$y : 15 x + 4 y \quad 3 x - y = 11$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{15\left(y+11\right)}{y+60y_{3}}\text{, }&y\neq -60y_{3}\\x\in \mathrm{C}\text{, }&y=-11\text{ and }y_{3}=\frac{11}{60}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15.

$$yx+60y_{3}x-15y=165$$

Add 15y to both sides.

$$yx+60y_{3}x=165+15y$$

Combine all terms containing x.

$$\left(y+60y_{3}\right)x=165+15y$$

The equation is in standard form.

$$\left(y+60y_{3}\right)x=15y+165$$

Divide both sides by y+60y_{3}.

$$\frac{\left(y+60y_{3}\right)x}{y+60y_{3}}=\frac{15y+165}{y+60y_{3}}$$

Dividing by y+60y_{3} undoes the multiplication by y+60y_{3}.

$$x=\frac{15y+165}{y+60y_{3}}$$

Divide 165+15y by y+60y_{3}.

$$x=\frac{15\left(y+11\right)}{y+60y_{3}}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{15\left(4xy_{3}-11\right)}{x-15}\text{, }&x\neq 15\\y\in \mathrm{C}\text{, }&y_{3}=\frac{11}{60}\text{ and }x=15\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15.

$$yx+60y_{3}x-15y=165$$

Subtract 60y_{3}x from both sides.

$$yx-15y=165-60y_{3}x$$

Combine all terms containing y.

$$\left(x-15\right)y=165-60y_{3}x$$

The equation is in standard form.

$$\left(x-15\right)y=165-60xy_{3}$$

Divide both sides by x-15.

$$\frac{\left(x-15\right)y}{x-15}=\frac{165-60xy_{3}}{x-15}$$

Dividing by x-15 undoes the multiplication by x-15.

$$y=\frac{165-60xy_{3}}{x-15}$$

Divide 165-60y_{3}x by x-15.

$$y=\frac{15\left(11-4xy_{3}\right)}{x-15}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{15\left(y+11\right)}{y+60y_{3}}\text{, }&y\neq -60y_{3}\\x\in \mathrm{R}\text{, }&y=-11\text{ and }y_{3}=\frac{11}{60}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15.

$$yx+60y_{3}x-15y=165$$

Add 15y to both sides.

$$yx+60y_{3}x=165+15y$$

Combine all terms containing x.

$$\left(y+60y_{3}\right)x=165+15y$$

The equation is in standard form.

$$\left(y+60y_{3}\right)x=15y+165$$

Divide both sides by y+60y_{3}.

$$\frac{\left(y+60y_{3}\right)x}{y+60y_{3}}=\frac{15y+165}{y+60y_{3}}$$

Dividing by y+60y_{3} undoes the multiplication by y+60y_{3}.

$$x=\frac{15y+165}{y+60y_{3}}$$

Divide 165+15y by y+60y_{3}.

$$x=\frac{15\left(y+11\right)}{y+60y_{3}}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{15\left(4xy_{3}-11\right)}{x-15}\text{, }&x\neq 15\\y\in \mathrm{R}\text{, }&y_{3}=\frac{11}{60}\text{ and }x=15\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15.

$$yx+60y_{3}x-15y=165$$

Subtract 60y_{3}x from both sides.

$$yx-15y=165-60y_{3}x$$

Combine all terms containing y.

$$\left(x-15\right)y=165-60y_{3}x$$

The equation is in standard form.

$$\left(x-15\right)y=165-60xy_{3}$$

Divide both sides by x-15.

$$\frac{\left(x-15\right)y}{x-15}=\frac{165-60xy_{3}}{x-15}$$

Dividing by x-15 undoes the multiplication by x-15.

$$y=\frac{165-60xy_{3}}{x-15}$$

Divide 165-60y_{3}x by x-15.

$$y=\frac{15\left(11-4xy_{3}\right)}{x-15}$$