Solve -(k-1)y=2x+5

$$- ( k - 1 ) y = 2 x + 5$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{-2x+y-5}{y}\text{, }&y\neq 0\\k\in \mathrm{C}\text{, }&x=-\frac{5}{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To find the opposite of k-1, find the opposite of each term.

$$\left(-k+1\right)y=2x+5$$

Use the distributive property to multiply -k+1 by y.

$$-ky+y=2x+5$$

Subtract y from both sides.

$$-ky=2x+5-y$$

The equation is in standard form.

$$\left(-y\right)k=2x-y+5$$

Divide both sides by -y.

$$\frac{\left(-y\right)k}{-y}=\frac{2x-y+5}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$k=\frac{2x-y+5}{-y}$$

Divide 2x+5-y by -y.

$$k=-\frac{2x+5}{y}+1$$

Solve for k

$$\left\{\begin{matrix}k=\frac{-2x+y-5}{y}\text{, }&y\neq 0\\k\in \mathrm{R}\text{, }&x=-\frac{5}{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To find the opposite of k-1, find the opposite of each term.

$$\left(-k+1\right)y=2x+5$$

Use the distributive property to multiply -k+1 by y.

$$-ky+y=2x+5$$

Subtract y from both sides.

$$-ky=2x+5-y$$

The equation is in standard form.

$$\left(-y\right)k=2x-y+5$$

Divide both sides by -y.

$$\frac{\left(-y\right)k}{-y}=\frac{2x-y+5}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$k=\frac{2x-y+5}{-y}$$

Divide 2x+5-y by -y.

$$k=-\frac{2x+5}{y}+1$$

Solve for x

$$x=\frac{-ky+y-5}{2}$$

Steps for Solving Linear Equation

To find the opposite of k-1, find the opposite of each term.

$$\left(-k+1\right)y=2x+5$$

Use the distributive property to multiply -k+1 by y.

$$-ky+y=2x+5$$

Swap sides so that all variable terms are on the left hand side.

$$2x+5=-ky+y$$

Subtract 5 from both sides.

$$2x=-ky+y-5$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{-ky+y-5}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{-ky+y-5}{2}$$