Solve 4-y/30-x=y-10/x-35

$$\frac{ 4-y }{ 30-x } = \frac{ y-10 }{ x-35 }$$

Solve for x

$$x=\frac{5\left(y+32\right)}{6}$$

$$y\neq 4\text{ and }y\neq 10$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 30,35 since division by zero is not defined. Multiply both sides of the equation by \left(x-35\right)\left(x-30\right), the least common multiple of 30-x,x-35.

$$\left(35-x\right)\left(4-y\right)=\left(x-30\right)\left(y-10\right)$$

Use the distributive property to multiply 35-x by 4-y.

$$140-35y-4x+yx=\left(x-30\right)\left(y-10\right)$$

Use the distributive property to multiply x-30 by y-10.

$$140-35y-4x+yx=xy-10x-30y+300$$

Subtract xy from both sides.

$$140-35y-4x+yx-xy=-10x-30y+300$$

Combine yx and -xy to get 0.

$$140-35y-4x=-10x-30y+300$$

Add 10x to both sides.

$$140-35y-4x+10x=-30y+300$$

Combine -4x and 10x to get 6x.

$$140-35y+6x=-30y+300$$

Subtract 140 from both sides.

$$-35y+6x=-30y+300-140$$

Subtract 140 from 300 to get 160.

$$-35y+6x=-30y+160$$

Add 35y to both sides.

$$6x=-30y+160+35y$$

Combine -30y and 35y to get 5y.

$$6x=5y+160$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{5y+160}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{5y+160}{6}$$

Divide 160+5y by 6.

$$x=\frac{5y}{6}+\frac{80}{3}$$

Variable x cannot be equal to any of the values 30,35.

$$x=\frac{5y}{6}+\frac{80}{3}\text{, }x\neq 30\text{ and }x\neq 35$$

Solve for y

$$y=\frac{6x}{5}-32$$

$$x\neq 30\text{ and }x\neq 35$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-35\right)\left(x-30\right), the least common multiple of 30-x,x-35.

$$\left(35-x\right)\left(4-y\right)=\left(x-30\right)\left(y-10\right)$$

Use the distributive property to multiply 35-x by 4-y.

$$140-35y-4x+yx=\left(x-30\right)\left(y-10\right)$$

Use the distributive property to multiply x-30 by y-10.

$$140-35y-4x+yx=xy-10x-30y+300$$

Subtract xy from both sides.

$$140-35y-4x+yx-xy=-10x-30y+300$$

Combine yx and -xy to get 0.

$$140-35y-4x=-10x-30y+300$$

Add 30y to both sides.

$$140-35y-4x+30y=-10x+300$$

Combine -35y and 30y to get -5y.

$$140-5y-4x=-10x+300$$

Subtract 140 from both sides.

$$-5y-4x=-10x+300-140$$

Subtract 140 from 300 to get 160.

$$-5y-4x=-10x+160$$

Add 4x to both sides.

$$-5y=-10x+160+4x$$

Combine -10x and 4x to get -6x.

$$-5y=-6x+160$$

The equation is in standard form.

$$-5y=160-6x$$

Divide both sides by -5.

$$\frac{-5y}{-5}=\frac{160-6x}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$y=\frac{160-6x}{-5}$$

Divide -6x+160 by -5.

$$y=\frac{6x}{5}-32$$