Solve (4-k)x+(1+k)y-3+2k=0

$$( 4 - k ) x + ( 1 + k ) y - 3 + 2 k = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{4x+y-3}{2+y-x}\text{, }&x\neq y+2\\k\in \mathrm{C}\text{, }&x=1\text{ and }y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4-k by x.

$$4x-kx+\left(1+k\right)y-3+2k=0$$

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

$$4x-kx+y+ky-3+2k=0$$

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

$$-kx+y+ky-3+2k=-4x$$

Subtract y from both sides.

$$-kx+ky-3+2k=-4x-y$$

Add 3 to both sides.

$$-kx+ky+2k=-4x-y+3$$

Combine all terms containing k.

$$\left(-x+y+2\right)k=-4x-y+3$$

The equation is in standard form.

$$\left(2+y-x\right)k=3-y-4x$$

Divide both sides by -x+y+2.

$$\frac{\left(2+y-x\right)k}{2+y-x}=\frac{3-y-4x}{2+y-x}$$

Dividing by -x+y+2 undoes the multiplication by -x+y+2.

$$k=\frac{3-y-4x}{2+y-x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{ky+y+2k-3}{4-k}\text{, }&k\neq 4\\x\in \mathrm{C}\text{, }&y=-1\text{ and }k=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4-k by x.

$$4x-kx+\left(1+k\right)y-3+2k=0$$

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

$$4x-kx+y+ky-3+2k=0$$

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

$$4x-kx+ky-3+2k=-y$$

Subtract ky from both sides.

$$4x-kx-3+2k=-y-ky$$

Add 3 to both sides.

$$4x-kx+2k=-y-ky+3$$

Subtract 2k from both sides.

$$4x-kx=-y-ky+3-2k$$

Combine all terms containing x.

$$\left(4-k\right)x=-y-ky+3-2k$$

The equation is in standard form.

$$\left(4-k\right)x=3-2k-y-ky$$

Divide both sides by 4-k.

$$\frac{\left(4-k\right)x}{4-k}=\frac{3-2k-y-ky}{4-k}$$

Dividing by 4-k undoes the multiplication by 4-k.

$$x=\frac{3-2k-y-ky}{4-k}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{4x+y-3}{2+y-x}\text{, }&x\neq y+2\\k\in \mathrm{R}\text{, }&x=1\text{ and }y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4-k by x.

$$4x-kx+\left(1+k\right)y-3+2k=0$$

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

$$4x-kx+y+ky-3+2k=0$$

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

$$-kx+y+ky-3+2k=-4x$$

Subtract y from both sides.

$$-kx+ky-3+2k=-4x-y$$

Add 3 to both sides.

$$-kx+ky+2k=-4x-y+3$$

Combine all terms containing k.

$$\left(-x+y+2\right)k=-4x-y+3$$

The equation is in standard form.

$$\left(2+y-x\right)k=3-y-4x$$

Divide both sides by -x+y+2.

$$\frac{\left(2+y-x\right)k}{2+y-x}=\frac{3-y-4x}{2+y-x}$$

Dividing by -x+y+2 undoes the multiplication by -x+y+2.

$$k=\frac{3-y-4x}{2+y-x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{ky+y+2k-3}{4-k}\text{, }&k\neq 4\\x\in \mathrm{R}\text{, }&y=-1\text{ and }k=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4-k by x.

$$4x-kx+\left(1+k\right)y-3+2k=0$$

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

$$4x-kx+y+ky-3+2k=0$$

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

$$4x-kx+ky-3+2k=-y$$

Subtract ky from both sides.

$$4x-kx-3+2k=-y-ky$$

Add 3 to both sides.

$$4x-kx+2k=-y-ky+3$$

Subtract 2k from both sides.

$$4x-kx=-y-ky+3-2k$$

Combine all terms containing x.

$$\left(4-k\right)x=-y-ky+3-2k$$

The equation is in standard form.

$$\left(4-k\right)x=3-2k-y-ky$$

Divide both sides by 4-k.

$$\frac{\left(4-k\right)x}{4-k}=\frac{3-2k-y-ky}{4-k}$$

Dividing by 4-k undoes the multiplication by 4-k.

$$x=\frac{3-2k-y-ky}{4-k}$$