Solve y=k(2x+1)+(1-k)(6x-2)

$$y = k ( 2 x + 1 ) + ( 1 - k ) ( 6 x - 2 )$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{2+y-6x}{4x-3}\text{, }&x\neq \frac{3}{4}\\k\in \mathrm{C}\text{, }&y=\frac{5}{2}\text{ and }x=\frac{3}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by 2x+1.

$$y=2kx+k+\left(1-k\right)\left(6x-2\right)$$

Use the distributive property to multiply 1-k by 6x-2.

$$y=2kx+k+6x-2-6kx+2k$$

Combine 2kx and -6kx to get -4kx.

$$y=-4kx+k+6x-2+2k$$

Combine k and 2k to get 3k.

$$y=-4kx+3k+6x-2$$

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

$$-4kx+3k+6x-2=y$$

Subtract 6x from both sides.

$$-4kx+3k-2=y-6x$$

Add 2 to both sides.

$$-4kx+3k=y-6x+2$$

Combine all terms containing k.

$$\left(-4x+3\right)k=y-6x+2$$

The equation is in standard form.

$$\left(3-4x\right)k=2+y-6x$$

Divide both sides by -4x+3.

$$\frac{\left(3-4x\right)k}{3-4x}=\frac{2+y-6x}{3-4x}$$

Dividing by -4x+3 undoes the multiplication by -4x+3.

$$k=\frac{2+y-6x}{3-4x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y-3k+2}{2\left(2k-3\right)}\text{, }&k\neq \frac{3}{2}\\x\in \mathrm{C}\text{, }&y=\frac{5}{2}\text{ and }k=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by 2x+1.

$$y=2kx+k+\left(1-k\right)\left(6x-2\right)$$

Use the distributive property to multiply 1-k by 6x-2.

$$y=2kx+k+6x-2-6kx+2k$$

Combine 2kx and -6kx to get -4kx.

$$y=-4kx+k+6x-2+2k$$

Combine k and 2k to get 3k.

$$y=-4kx+3k+6x-2$$

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

$$-4kx+3k+6x-2=y$$

Subtract 3k from both sides.

$$-4kx+6x-2=y-3k$$

Add 2 to both sides.

$$-4kx+6x=y-3k+2$$

Combine all terms containing x.

$$\left(-4k+6\right)x=y-3k+2$$

The equation is in standard form.

$$\left(6-4k\right)x=y-3k+2$$

Divide both sides by -4k+6.

$$\frac{\left(6-4k\right)x}{6-4k}=\frac{y-3k+2}{6-4k}$$

Dividing by -4k+6 undoes the multiplication by -4k+6.

$$x=\frac{y-3k+2}{6-4k}$$

Divide y-3k+2 by -4k+6.

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

Solve for k

$$\left\{\begin{matrix}k=-\frac{2+y-6x}{4x-3}\text{, }&x\neq \frac{3}{4}\\k\in \mathrm{R}\text{, }&y=\frac{5}{2}\text{ and }x=\frac{3}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by 2x+1.

$$y=2kx+k+\left(1-k\right)\left(6x-2\right)$$

Use the distributive property to multiply 1-k by 6x-2.

$$y=2kx+k+6x-2-6kx+2k$$

Combine 2kx and -6kx to get -4kx.

$$y=-4kx+k+6x-2+2k$$

Combine k and 2k to get 3k.

$$y=-4kx+3k+6x-2$$

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

$$-4kx+3k+6x-2=y$$

Subtract 6x from both sides.

$$-4kx+3k-2=y-6x$$

Add 2 to both sides.

$$-4kx+3k=y-6x+2$$

Combine all terms containing k.

$$\left(-4x+3\right)k=y-6x+2$$

The equation is in standard form.

$$\left(3-4x\right)k=2+y-6x$$

Divide both sides by -4x+3.

$$\frac{\left(3-4x\right)k}{3-4x}=\frac{2+y-6x}{3-4x}$$

Dividing by -4x+3 undoes the multiplication by -4x+3.

$$k=\frac{2+y-6x}{3-4x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y-3k+2}{2\left(2k-3\right)}\text{, }&k\neq \frac{3}{2}\\x\in \mathrm{R}\text{, }&y=\frac{5}{2}\text{ and }k=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k by 2x+1.

$$y=2kx+k+\left(1-k\right)\left(6x-2\right)$$

Use the distributive property to multiply 1-k by 6x-2.

$$y=2kx+k+6x-2-6kx+2k$$

Combine 2kx and -6kx to get -4kx.

$$y=-4kx+k+6x-2+2k$$

Combine k and 2k to get 3k.

$$y=-4kx+3k+6x-2$$

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

$$-4kx+3k+6x-2=y$$

Subtract 3k from both sides.

$$-4kx+6x-2=y-3k$$

Add 2 to both sides.

$$-4kx+6x=y-3k+2$$

Combine all terms containing x.

$$\left(-4k+6\right)x=y-3k+2$$

The equation is in standard form.

$$\left(6-4k\right)x=y-3k+2$$

Divide both sides by -4k+6.

$$\frac{\left(6-4k\right)x}{6-4k}=\frac{y-3k+2}{6-4k}$$

Dividing by -4k+6 undoes the multiplication by -4k+6.

$$x=\frac{y-3k+2}{6-4k}$$

Divide y-3k+2 by -4k+6.

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