Solve xy-1/2-6x-1/3=10

$$\frac { x y - 1 } { 2 } - \frac { 6 x - 1 } { 3 } = 10$$

Solve for x

$$x=\frac{61}{3\left(y-4\right)}$$

$$y\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(xy-1\right)-2\left(6x-1\right)=60$$

Use the distributive property to multiply 3 by xy-1.

$$3xy-3-2\left(6x-1\right)=60$$

Use the distributive property to multiply -2 by 6x-1.

$$3xy-3-12x+2=60$$

Add -3 and 2 to get -1.

$$3xy-1-12x=60$$

Add 1 to both sides.

$$3xy-12x=60+1$$

Add 60 and 1 to get 61.

$$3xy-12x=61$$

Combine all terms containing x.

$$\left(3y-12\right)x=61$$

Divide both sides by 3y-12.

$$\frac{\left(3y-12\right)x}{3y-12}=\frac{61}{3y-12}$$

Dividing by 3y-12 undoes the multiplication by 3y-12.

$$x=\frac{61}{3y-12}$$

Divide 61 by 3y-12.

$$x=\frac{61}{3\left(y-4\right)}$$

Solve for y

$$y=4+\frac{61}{3x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(xy-1\right)-2\left(6x-1\right)=60$$

Use the distributive property to multiply 3 by xy-1.

$$3xy-3-2\left(6x-1\right)=60$$

Use the distributive property to multiply -2 by 6x-1.

$$3xy-3-12x+2=60$$

Add -3 and 2 to get -1.

$$3xy-1-12x=60$$

Add 1 to both sides.

$$3xy-12x=60+1$$

Add 60 and 1 to get 61.

$$3xy-12x=61$$

Add 12x to both sides.

$$3xy=61+12x$$

The equation is in standard form.

$$3xy=12x+61$$

Divide both sides by 3x.

$$\frac{3xy}{3x}=\frac{12x+61}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$y=\frac{12x+61}{3x}$$

Divide 61+12x by 3x.

$$y=4+\frac{61}{3x}$$