Solve -3(x+ay+11)-4(2-bx)=33x+15y-c

$$- 3 ( x + a y + 11 ) - 4 ( 2 - b x ) = 33 x + 15 y - c$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{41-c+15y+36x-4bx}{3y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&c=41+36x-4bx\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x+ay+11.

$$-3x-3ay-33-4\left(2-bx\right)=33x+15y-c$$

Use the distributive property to multiply -4 by 2-bx.

$$-3x-3ay-33-8+4bx=33x+15y-c$$

Subtract 8 from -33 to get -41.

$$-3x-3ay-41+4bx=33x+15y-c$$

Add 3x to both sides.

$$-3ay-41+4bx=33x+15y-c+3x$$

Combine 33x and 3x to get 36x.

$$-3ay-41+4bx=36x+15y-c$$

Add 41 to both sides.

$$-3ay+4bx=36x+15y-c+41$$

Subtract 4bx from both sides.

$$-3ay=36x+15y-c+41-4bx$$

The equation is in standard form.

$$\left(-3y\right)a=41-c+15y+36x-4bx$$

Divide both sides by -3y.

$$\frac{\left(-3y\right)a}{-3y}=\frac{41-c+15y+36x-4bx}{-3y}$$

Dividing by -3y undoes the multiplication by -3y.

$$a=\frac{41-c+15y+36x-4bx}{-3y}$$

Divide 36x+15y-c+41-4bx by -3y.

$$a=-\frac{41-c+15y+36x-4bx}{3y}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{36x+3ay+15y-c+41}{4x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=3ay+15y+41\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x+ay+11.

$$-3x-3ay-33-4\left(2-bx\right)=33x+15y-c$$

Use the distributive property to multiply -4 by 2-bx.

$$-3x-3ay-33-8+4bx=33x+15y-c$$

Subtract 8 from -33 to get -41.

$$-3x-3ay-41+4bx=33x+15y-c$$

Add 3x to both sides.

$$-3ay-41+4bx=33x+15y-c+3x$$

Combine 33x and 3x to get 36x.

$$-3ay-41+4bx=36x+15y-c$$

Add 3ay to both sides.

$$-41+4bx=36x+15y-c+3ay$$

Add 41 to both sides.

$$4bx=36x+15y-c+3ay+41$$

The equation is in standard form.

$$4xb=36x+3ay+15y-c+41$$

Divide both sides by 4x.

$$\frac{4xb}{4x}=\frac{36x+3ay+15y-c+41}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$b=\frac{36x+3ay+15y-c+41}{4x}$$