Solve y-6/x=9/15

$$y - \frac { 6 } { x } = \frac { 9 } { 15 }$$

Solve for x

$$x=-\frac{30}{3-5y}$$

$$y\neq \frac{3}{5}$$

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 15x, the least common multiple of x,15.

$$15xy-15\times 6=x\times 9$$

Multiply -15 and 6 to get -90.

$$15xy-90=x\times 9$$

Subtract x\times 9 from both sides.

$$15xy-90-x\times 9=0$$

Multiply -1 and 9 to get -9.

$$15xy-90-9x=0$$

Add 90 to both sides. Anything plus zero gives itself.

$$15xy-9x=90$$

Combine all terms containing x.

$$\left(15y-9\right)x=90$$

Divide both sides by 15y-9.

$$\frac{\left(15y-9\right)x}{15y-9}=\frac{90}{15y-9}$$

Dividing by 15y-9 undoes the multiplication by 15y-9.

$$x=\frac{90}{15y-9}$$

Divide 90 by 15y-9.

$$x=\frac{30}{5y-3}$$

Variable x cannot be equal to 0.

$$x=\frac{30}{5y-3}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15x, the least common multiple of x,15.

$$15xy-15\times 6=x\times 9$$

Multiply -15 and 6 to get -90.

$$15xy-90=x\times 9$$

Add 90 to both sides.

$$15xy=x\times 9+90$$

The equation is in standard form.

$$15xy=9x+90$$

Divide both sides by 15x.

$$\frac{15xy}{15x}=\frac{9x+90}{15x}$$

Dividing by 15x undoes the multiplication by 15x.

$$y=\frac{9x+90}{15x}$$

Divide 90+9x by 15x.

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