Solve 22*16+22*8*y/x=54+y/2x*9

$$22 \times 16 + 22 \times 8 \times \frac { y } { x } = 54 + \frac { y } { 2 x } \times 9$$

Solve for x

$$x=-\frac{343y}{596}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of x,2x.

$$22\times 16\times 2x+22\times 8\times 2y=2x\times 54+y\times 9$$

Do the multiplications.

$$352\times 2x+176\times 2y=2x\times 54+y\times 9$$

Multiply 352 and 2 to get 704.

$$704x+176\times 2y=2x\times 54+y\times 9$$

Multiply 176 and 2 to get 352.

$$704x+352y=2x\times 54+y\times 9$$

Multiply 2 and 54 to get 108.

$$704x+352y=108x+y\times 9$$

Subtract 108x from both sides.

$$704x+352y-108x=y\times 9$$

Combine 704x and -108x to get 596x.

$$596x+352y=y\times 9$$

Subtract 352y from both sides.

$$596x=y\times 9-352y$$

Combine y\times 9 and -352y to get -343y.

$$596x=-343y$$

Divide both sides by 596.

$$\frac{596x}{596}=-\frac{343y}{596}$$

Dividing by 596 undoes the multiplication by 596.

$$x=-\frac{343y}{596}$$

Variable x cannot be equal to 0.

$$x=-\frac{343y}{596}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{596x}{343}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x, the least common multiple of x,2x.

$$22\times 16\times 2x+22\times 8\times 2y=2x\times 54+y\times 9$$

Do the multiplications.

$$352\times 2x+176\times 2y=2x\times 54+y\times 9$$

Multiply 352 and 2 to get 704.

$$704x+176\times 2y=2x\times 54+y\times 9$$

Multiply 176 and 2 to get 352.

$$704x+352y=2x\times 54+y\times 9$$

Multiply 2 and 54 to get 108.

$$704x+352y=108x+y\times 9$$

Subtract y\times 9 from both sides.

$$704x+352y-y\times 9=108x$$

Combine 352y and -y\times 9 to get 343y.

$$704x+343y=108x$$

Subtract 704x from both sides.

$$343y=108x-704x$$

Combine 108x and -704x to get -596x.

$$343y=-596x$$

Divide both sides by 343.

$$\frac{343y}{343}=-\frac{596x}{343}$$

Dividing by 343 undoes the multiplication by 343.

$$y=-\frac{596x}{343}$$