Solve y-6/-y+4=x-48/120-48

$$\frac { y - 6 } { - y + 4 } = \frac { x - 48 } { 120 - 48 }$$

Solve for x

$$x=-\frac{24\left(y-10\right)}{y-4}$$

$$y\neq 4$$

Steps for Solving Linear Equation

Subtract 48 from 120 to get 72.

$$\frac{y-6}{-y+4}=\frac{x-48}{72}$$

Divide each term of x-48 by 72 to get \frac{1}{72}x-\frac{2}{3}.

$$\frac{y-6}{-y+4}=\frac{1}{72}x-\frac{2}{3}$$

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

$$\frac{1}{72}x-\frac{2}{3}=\frac{y-6}{-y+4}$$

Add \frac{2}{3} to both sides.

$$\frac{1}{72}x=\frac{y-6}{-y+4}+\frac{2}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -y+4 and 3 is 3\left(4-y\right). Multiply \frac{y-6}{-y+4} times \frac{3}{3}. Multiply \frac{2}{3} times \frac{4-y}{4-y}.

$$\frac{1}{72}x=\frac{3\left(y-6\right)}{3\left(4-y\right)}+\frac{2\left(4-y\right)}{3\left(4-y\right)}$$

Since \frac{3\left(y-6\right)}{3\left(4-y\right)} and \frac{2\left(4-y\right)}{3\left(4-y\right)} have the same denominator, add them by adding their numerators.

$$\frac{1}{72}x=\frac{3\left(y-6\right)+2\left(4-y\right)}{3\left(4-y\right)}$$

Do the multiplications in 3\left(y-6\right)+2\left(4-y\right).

$$\frac{1}{72}x=\frac{3y-18+8-2y}{3\left(4-y\right)}$$

Combine like terms in 3y-18+8-2y.

$$\frac{1}{72}x=\frac{y-10}{3\left(4-y\right)}$$

Multiply both sides of the equation by 72\left(y-4\right), the least common multiple of 72,3\left(4-y\right).

$$\frac{1}{72}x\times 72\left(y-4\right)=-24\left(y-10\right)$$

Multiply \frac{1}{72} and 72 to get 1.

$$x\left(y-4\right)=-24\left(y-10\right)$$

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

$$xy-4x=-24\left(y-10\right)$$

Use the distributive property to multiply -24 by y-10.

$$xy-4x=-24y+240$$

Combine all terms containing x.

$$\left(y-4\right)x=-24y+240$$

The equation is in standard form.

$$\left(y-4\right)x=240-24y$$

Divide both sides by y-4.

$$\frac{\left(y-4\right)x}{y-4}=\frac{240-24y}{y-4}$$

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

$$x=\frac{240-24y}{y-4}$$

Divide -24y+240 by y-4.

$$x=\frac{24\left(10-y\right)}{y-4}$$

Solve for y

$$y=\frac{4\left(x+60\right)}{x+24}$$

$$x\neq -24$$

Steps for Solving Linear Equation

Subtract 48 from 120 to get 72.

$$\frac{y-6}{-y+4}=\frac{x-48}{72}$$

Divide each term of x-48 by 72 to get \frac{1}{72}x-\frac{2}{3}.

$$\frac{y-6}{-y+4}=\frac{1}{72}x-\frac{2}{3}$$

Variable y cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by 72\left(y-4\right), the least common multiple of -y+4,72,3.

$$-72\left(y-6\right)=\frac{1}{72}x\times 72\left(y-4\right)+72\left(y-4\right)\left(-\frac{2}{3}\right)$$

Use the distributive property to multiply -72 by y-6.

$$-72y+432=\frac{1}{72}x\times 72\left(y-4\right)+72\left(y-4\right)\left(-\frac{2}{3}\right)$$

Multiply \frac{1}{72} and 72 to get 1.

$$-72y+432=x\left(y-4\right)+72\left(y-4\right)\left(-\frac{2}{3}\right)$$

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

$$-72y+432=xy-4x+72\left(y-4\right)\left(-\frac{2}{3}\right)$$

Multiply 72 and -\frac{2}{3} to get -48.

$$-72y+432=xy-4x-48\left(y-4\right)$$

Use the distributive property to multiply -48 by y-4.

$$-72y+432=xy-4x-48y+192$$

Subtract xy from both sides.

$$-72y+432-xy=-4x-48y+192$$

Add 48y to both sides.

$$-72y+432-xy+48y=-4x+192$$

Combine -72y and 48y to get -24y.

$$-24y+432-xy=-4x+192$$

Subtract 432 from both sides.

$$-24y-xy=-4x+192-432$$

Subtract 432 from 192 to get -240.

$$-24y-xy=-4x-240$$

Combine all terms containing y.

$$\left(-24-x\right)y=-4x-240$$

The equation is in standard form.

$$\left(-x-24\right)y=-4x-240$$

Divide both sides by -24-x.

$$\frac{\left(-x-24\right)y}{-x-24}=\frac{-4x-240}{-x-24}$$

Dividing by -24-x undoes the multiplication by -24-x.

$$y=\frac{-4x-240}{-x-24}$$

Divide -4x-240 by -24-x.

$$y=\frac{4\left(x+60\right)}{x+24}$$

Variable y cannot be equal to 4.

$$y=\frac{4\left(x+60\right)}{x+24}\text{, }y\neq 4$$