Solve 1.5*12y/12-x+4y=34

$$\frac{ 1.5 \cdot 12y }{ 12-x } +4y = 34$$

Solve for x

$$x=-\frac{3\left(11y-68\right)}{17-2y}$$

$$y\neq 0\text{ and }y\neq \frac{17}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 12 since division by zero is not defined. Multiply both sides of the equation by -x+12.

$$1.5\times 12y+4y\left(-x+12\right)=34\left(-x+12\right)$$

Multiply 1.5 and 12 to get 18.

$$18y+4y\left(-x+12\right)=34\left(-x+12\right)$$

Use the distributive property to multiply 4y by -x+12.

$$18y-4xy+48y=34\left(-x+12\right)$$

Combine 18y and 48y to get 66y.

$$66y-4xy=34\left(-x+12\right)$$

Use the distributive property to multiply 34 by -x+12.

$$66y-4xy=-34x+408$$

Add 34x to both sides.

$$66y-4xy+34x=408$$

Subtract 66y from both sides.

$$-4xy+34x=408-66y$$

Combine all terms containing x.

$$\left(-4y+34\right)x=408-66y$$

The equation is in standard form.

$$\left(34-4y\right)x=408-66y$$

Divide both sides by -4y+34.

$$\frac{\left(34-4y\right)x}{34-4y}=\frac{408-66y}{34-4y}$$

Dividing by -4y+34 undoes the multiplication by -4y+34.

$$x=\frac{408-66y}{34-4y}$$

Divide 408-66y by -4y+34.

$$x=\frac{3\left(68-11y\right)}{17-2y}$$

Variable x cannot be equal to 12.

$$x=\frac{3\left(68-11y\right)}{17-2y}\text{, }x\neq 12$$

Solve for y

$$y=-\frac{17\left(x-12\right)}{33-2x}$$

$$x\neq \frac{33}{2}\text{ and }x\neq 12$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -x+12.

$$1.5\times 12y+4y\left(-x+12\right)=34\left(-x+12\right)$$

Multiply 1.5 and 12 to get 18.

$$18y+4y\left(-x+12\right)=34\left(-x+12\right)$$

Use the distributive property to multiply 4y by -x+12.

$$18y-4xy+48y=34\left(-x+12\right)$$

Combine 18y and 48y to get 66y.

$$66y-4xy=34\left(-x+12\right)$$

Use the distributive property to multiply 34 by -x+12.

$$66y-4xy=-34x+408$$

Combine all terms containing y.

$$\left(66-4x\right)y=-34x+408$$

The equation is in standard form.

$$\left(66-4x\right)y=408-34x$$

Divide both sides by 66-4x.

$$\frac{\left(66-4x\right)y}{66-4x}=\frac{408-34x}{66-4x}$$

Dividing by 66-4x undoes the multiplication by 66-4x.

$$y=\frac{408-34x}{66-4x}$$

Divide -34x+408 by 66-4x.

$$y=\frac{17\left(12-x\right)}{33-2x}$$