Solve x-7/2-y-7/3=-13/36

$$\frac { x - 7 } { 2 } - \frac { y - 7 } { 3 } = - \frac { 13 } { 36 }$$

Solve for x

$$x=\frac{2y}{3}+\frac{29}{18}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 2,3,36.

$$18\left(x-7\right)-12\left(y-7\right)=-13$$

Use the distributive property to multiply 18 by x-7.

$$18x-126-12\left(y-7\right)=-13$$

Use the distributive property to multiply -12 by y-7.

$$18x-126-12y+84=-13$$

Add -126 and 84 to get -42.

$$18x-42-12y=-13$$

Add 42 to both sides.

$$18x-12y=-13+42$$

Add -13 and 42 to get 29.

$$18x-12y=29$$

Add 12y to both sides.

$$18x=29+12y$$

The equation is in standard form.

$$18x=12y+29$$

Divide both sides by 18.

$$\frac{18x}{18}=\frac{12y+29}{18}$$

Dividing by 18 undoes the multiplication by 18.

$$x=\frac{12y+29}{18}$$

Divide 29+12y by 18.

$$x=\frac{2y}{3}+\frac{29}{18}$$

Solve for y

$$y=\frac{3x}{2}-\frac{29}{12}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 2,3,36.

$$18\left(x-7\right)-12\left(y-7\right)=-13$$

Use the distributive property to multiply 18 by x-7.

$$18x-126-12\left(y-7\right)=-13$$

Use the distributive property to multiply -12 by y-7.

$$18x-126-12y+84=-13$$

Add -126 and 84 to get -42.

$$18x-42-12y=-13$$

Subtract 18x from both sides.

$$-42-12y=-13-18x$$

Add 42 to both sides.

$$-12y=-13-18x+42$$

Add -13 and 42 to get 29.

$$-12y=29-18x$$

Divide both sides by -12.

$$\frac{-12y}{-12}=\frac{29-18x}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$y=\frac{29-18x}{-12}$$

Divide 29-18x by -12.

$$y=\frac{3x}{2}-\frac{29}{12}$$