Solve x-4/2-y-5/3=0

$$\frac { x - 4 } { 2 } - \frac { y - 5 } { 3 } = 0$$

Solve for x

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

Steps for Solving Linear Equation

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

$$3\left(x-4\right)-2\left(y-5\right)=0$$

Use the distributive property to multiply 3 by x-4.

$$3x-12-2\left(y-5\right)=0$$

Use the distributive property to multiply -2 by y-5.

$$3x-12-2y+10=0$$

Add -12 and 10 to get -2.

$$3x-2-2y=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$3x-2y=2$$

Add 2y to both sides.

$$3x=2+2y$$

The equation is in standard form.

$$3x=2y+2$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{2y+2}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{2y+2}{3}$$

Solve for y

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

Steps for Solving Linear Equation

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

$$3\left(x-4\right)-2\left(y-5\right)=0$$

Use the distributive property to multiply 3 by x-4.

$$3x-12-2\left(y-5\right)=0$$

Use the distributive property to multiply -2 by y-5.

$$3x-12-2y+10=0$$

Add -12 and 10 to get -2.

$$3x-2-2y=0$$

Subtract 3x from both sides. Anything subtracted from zero gives its negation.

$$-2-2y=-3x$$

Add 2 to both sides.

$$-2y=-3x+2$$

The equation is in standard form.

$$-2y=2-3x$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{2-3x}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{2-3x}{-2}$$

Divide -3x+2 by -2.

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