Solve left(k+1right)x+4y-7=0

$$\left( k+1 \right) x+4y-7 = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{x+4y-7}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&y=\frac{7}{4}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k+1 by x.

$$kx+x+4y-7=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$kx+4y-7=-x$$

Subtract 4y from both sides.

$$kx-7=-x-4y$$

Add 7 to both sides.

$$kx=-x-4y+7$$

The equation is in standard form.

$$xk=7-4y-x$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{7-4y-x}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{7-4y-x}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{4y-7}{k+1}\text{, }&k\neq -1\\x\in \mathrm{C}\text{, }&y=\frac{7}{4}\text{ and }k=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k+1 by x.

$$kx+x+4y-7=0$$

Subtract 4y from both sides. Anything subtracted from zero gives its negation.

$$kx+x-7=-4y$$

Add 7 to both sides.

$$kx+x=-4y+7$$

Combine all terms containing x.

$$\left(k+1\right)x=-4y+7$$

The equation is in standard form.

$$\left(k+1\right)x=7-4y$$

Divide both sides by k+1.

$$\frac{\left(k+1\right)x}{k+1}=\frac{7-4y}{k+1}$$

Dividing by k+1 undoes the multiplication by k+1.

$$x=\frac{7-4y}{k+1}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{x+4y-7}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=\frac{7}{4}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k+1 by x.

$$kx+x+4y-7=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$kx+4y-7=-x$$

Subtract 4y from both sides.

$$kx-7=-x-4y$$

Add 7 to both sides.

$$kx=-x-4y+7$$

The equation is in standard form.

$$xk=7-4y-x$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{7-4y-x}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{7-4y-x}{x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{4y-7}{k+1}\text{, }&k\neq -1\\x\in \mathrm{R}\text{, }&y=\frac{7}{4}\text{ and }k=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k+1 by x.

$$kx+x+4y-7=0$$

Subtract 4y from both sides. Anything subtracted from zero gives its negation.

$$kx+x-7=-4y$$

Add 7 to both sides.

$$kx+x=-4y+7$$

Combine all terms containing x.

$$\left(k+1\right)x=-4y+7$$

The equation is in standard form.

$$\left(k+1\right)x=7-4y$$

Divide both sides by k+1.

$$\frac{\left(k+1\right)x}{k+1}=\frac{7-4y}{k+1}$$

Dividing by k+1 undoes the multiplication by k+1.

$$x=\frac{7-4y}{k+1}$$