Solve =10(y-4)+8quad(9)x-9/x-5=5/7

$$= 10 ( y - 4 ) + 8 \quad ( 9 ) \frac { x - 9 } { x - 5 } = \frac { 5 } { 7 }$$

Solve for x

$$x=\frac{350y+3111}{70y+219}$$

$$y\neq -\frac{219}{70}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 7\left(x-5\right), the least common multiple of x-5,7.

$$10\left(y-4\right)\times 7\left(x-5\right)+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Multiply 10 and 7 to get 70.

$$70\left(y-4\right)\left(x-5\right)+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Use the distributive property to multiply 70 by y-4.

$$\left(70y-280\right)\left(x-5\right)+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Use the distributive property to multiply 70y-280 by x-5.

$$70yx-350y-280x+1400+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Multiply 8 and 9 to get 72.

$$70yx-350y-280x+1400+72\times 7\left(x-9\right)=5\left(x-5\right)$$

Multiply 72 and 7 to get 504.

$$70yx-350y-280x+1400+504\left(x-9\right)=5\left(x-5\right)$$

Use the distributive property to multiply 504 by x-9.

$$70yx-350y-280x+1400+504x-4536=5\left(x-5\right)$$

Combine -280x and 504x to get 224x.

$$70yx-350y+224x+1400-4536=5\left(x-5\right)$$

Subtract 4536 from 1400 to get -3136.

$$70yx-350y+224x-3136=5\left(x-5\right)$$

Use the distributive property to multiply 5 by x-5.

$$70yx-350y+224x-3136=5x-25$$

Subtract 5x from both sides.

$$70yx-350y+224x-3136-5x=-25$$

Combine 224x and -5x to get 219x.

$$70yx-350y+219x-3136=-25$$

Add 350y to both sides.

$$70yx+219x-3136=-25+350y$$

Add 3136 to both sides.

$$70yx+219x=-25+350y+3136$$

Add -25 and 3136 to get 3111.

$$70yx+219x=3111+350y$$

Combine all terms containing x.

$$\left(70y+219\right)x=3111+350y$$

The equation is in standard form.

$$\left(70y+219\right)x=350y+3111$$

Divide both sides by 70y+219.

$$\frac{\left(70y+219\right)x}{70y+219}=\frac{350y+3111}{70y+219}$$

Dividing by 70y+219 undoes the multiplication by 70y+219.

$$x=\frac{350y+3111}{70y+219}$$

Variable x cannot be equal to 5.

$$x=\frac{350y+3111}{70y+219}\text{, }x\neq 5$$

Solve for y

$$y=-\frac{3\left(73x-1037\right)}{70\left(x-5\right)}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7\left(x-5\right), the least common multiple of x-5,7.

$$10\left(y-4\right)\times 7\left(x-5\right)+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Multiply 10 and 7 to get 70.

$$70\left(y-4\right)\left(x-5\right)+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Use the distributive property to multiply 70 by y-4.

$$\left(70y-280\right)\left(x-5\right)+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Use the distributive property to multiply 70y-280 by x-5.

$$70yx-350y-280x+1400+8\times 9\times 7\left(x-9\right)=5\left(x-5\right)$$

Multiply 8 and 9 to get 72.

$$70yx-350y-280x+1400+72\times 7\left(x-9\right)=5\left(x-5\right)$$

Multiply 72 and 7 to get 504.

$$70yx-350y-280x+1400+504\left(x-9\right)=5\left(x-5\right)$$

Use the distributive property to multiply 504 by x-9.

$$70yx-350y-280x+1400+504x-4536=5\left(x-5\right)$$

Combine -280x and 504x to get 224x.

$$70yx-350y+224x+1400-4536=5\left(x-5\right)$$

Subtract 4536 from 1400 to get -3136.

$$70yx-350y+224x-3136=5\left(x-5\right)$$

Use the distributive property to multiply 5 by x-5.

$$70yx-350y+224x-3136=5x-25$$

Subtract 224x from both sides.

$$70yx-350y-3136=5x-25-224x$$

Combine 5x and -224x to get -219x.

$$70yx-350y-3136=-219x-25$$

Add 3136 to both sides.

$$70yx-350y=-219x-25+3136$$

Add -25 and 3136 to get 3111.

$$70yx-350y=-219x+3111$$

Combine all terms containing y.

$$\left(70x-350\right)y=-219x+3111$$

The equation is in standard form.

$$\left(70x-350\right)y=3111-219x$$

Divide both sides by 70x-350.

$$\frac{\left(70x-350\right)y}{70x-350}=\frac{3111-219x}{70x-350}$$

Dividing by 70x-350 undoes the multiplication by 70x-350.

$$y=\frac{3111-219x}{70x-350}$$

Divide -219x+3111 by 70x-350.

$$y=\frac{3\left(1037-73x\right)}{70\left(x-5\right)}$$