Solve 2ax+2(b+b)=-3x+4by-17

$$2 a x + 2 ( b + b ) = - 3 x + 4 b y - 17$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{3x-4by+4b+17}{2x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=\frac{17}{4\left(y-1\right)}\text{ and }y\neq 1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine b and b to get 2b.

$$2ax+2\times 2b=-3x+4by-17$$

Multiply 2 and 2 to get 4.

$$2ax+4b=-3x+4by-17$$

Subtract 4b from both sides.

$$2ax=-3x+4by-17-4b$$

The equation is in standard form.

$$2xa=-3x+4by-4b-17$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-3x+4by-4b-17}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-3x+4by-4b-17}{2x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{2ax+3x+17}{4\left(1-y\right)}\text{, }&y\neq 1\\b\in \mathrm{C}\text{, }&a=-\frac{3}{2}-\frac{17}{2x}\text{ and }x\neq 0\text{ and }y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine b and b to get 2b.

$$2ax+2\times 2b=-3x+4by-17$$

Multiply 2 and 2 to get 4.

$$2ax+4b=-3x+4by-17$$

Subtract 4by from both sides.

$$2ax+4b-4by=-3x-17$$

Subtract 2ax from both sides.

$$4b-4by=-3x-17-2ax$$

Combine all terms containing b.

$$\left(4-4y\right)b=-3x-17-2ax$$

The equation is in standard form.

$$\left(4-4y\right)b=-2ax-3x-17$$

Divide both sides by -4y+4.

$$\frac{\left(4-4y\right)b}{4-4y}=\frac{-2ax-3x-17}{4-4y}$$

Dividing by -4y+4 undoes the multiplication by -4y+4.

$$b=\frac{-2ax-3x-17}{4-4y}$$

Divide -3x-17-2ax by -4y+4.

$$b=-\frac{2ax+3x+17}{4\left(1-y\right)}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{3x-4by+4b+17}{2x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=\frac{17}{4\left(y-1\right)}\text{ and }y\neq 1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine b and b to get 2b.

$$2ax+2\times 2b=-3x+4by-17$$

Multiply 2 and 2 to get 4.

$$2ax+4b=-3x+4by-17$$

Subtract 4b from both sides.

$$2ax=-3x+4by-17-4b$$

The equation is in standard form.

$$2xa=-3x+4by-4b-17$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-3x+4by-4b-17}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-3x+4by-4b-17}{2x}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{2ax+3x+17}{4\left(1-y\right)}\text{, }&y\neq 1\\b\in \mathrm{R}\text{, }&a=-\frac{3}{2}-\frac{17}{2x}\text{ and }x\neq 0\text{ and }y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine b and b to get 2b.

$$2ax+2\times 2b=-3x+4by-17$$

Multiply 2 and 2 to get 4.

$$2ax+4b=-3x+4by-17$$

Subtract 4by from both sides.

$$2ax+4b-4by=-3x-17$$

Subtract 2ax from both sides.

$$4b-4by=-3x-17-2ax$$

Combine all terms containing b.

$$\left(4-4y\right)b=-3x-17-2ax$$

The equation is in standard form.

$$\left(4-4y\right)b=-2ax-3x-17$$

Divide both sides by -4y+4.

$$\frac{\left(4-4y\right)b}{4-4y}=\frac{-2ax-3x-17}{4-4y}$$

Dividing by -4y+4 undoes the multiplication by -4y+4.

$$b=\frac{-2ax-3x-17}{4-4y}$$

Divide -3x-17-2ax by -4y+4.

$$b=-\frac{2ax+3x+17}{4\left(1-y\right)}$$