Solve 2x+3y=sqrt{3+x}

$$2 x + 3 y = \sqrt { 3 + x }$$

Solve for y (complex solution)

$$y=\frac{-2x+\sqrt{x+3}}{3}$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$3y=\sqrt{3+x}-2x$$

The equation is in standard form.

$$3y=-2x+\sqrt{x+3}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{-2x+\sqrt{x+3}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{-2x+\sqrt{x+3}}{3}$$

Solve for y

$$y=\frac{-2x+\sqrt{x+3}}{3}$$

$$x\geq -3$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$3y=\sqrt{3+x}-2x$$

The equation is in standard form.

$$3y=-2x+\sqrt{x+3}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{-2x+\sqrt{x+3}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{-2x+\sqrt{x+3}}{3}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{3y}{2}+\frac{\sqrt{49-24y}}{8}+\frac{1}{8}\text{, }&arg(\frac{\sqrt{49-24y}+1}{4})<\pi \\x=-\frac{3y}{2}-\frac{\sqrt{49-24y}}{8}+\frac{1}{8}\text{, }&y=2\text{ or }arg(\frac{-\sqrt{49-24y}+1}{4})<\pi \end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{3y}{2}+\frac{\sqrt{49-24y}}{8}+\frac{1}{8}\text{, }&y\leq \frac{49}{24}\\x=-\frac{3y}{2}-\frac{\sqrt{49-24y}}{8}+\frac{1}{8}\text{, }&y\geq 2\text{ and }y\leq \frac{49}{24}\end{matrix}\right.$$