Solve {l}{x-1/2-y-1/3=-13/36(1)}{x-11/3+frac{9+1}{2}=-frac{2}{3}}

$$\left. \begin{array} { l } { \frac { x - 1 } { 2 } - \frac { y - 1 } { 3 } = - \frac { 13 } { 36 } ( 1 ) } \\ { x - \frac { 11 } { 3 } + \frac { 9 + 1 } { 2 } = - \frac { 2 } { 3 } } \end{array} \right.$$

Solve for x, y

$$x=-2$$

$$y = -\frac{29}{12} = -2\frac{5}{12} \approx -2.416666667$$

Solution Steps

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

$$6x-22+3\left(9+1\right)=-4$$

Add 9 and 1 to get 10.

$$6x-22+3\times 10=-4$$

Multiply 3 and 10 to get 30.

$$6x-22+30=-4$$

Add -22 and 30 to get 8.

$$6x+8=-4$$

Subtract 8 from both sides.

$$6x=-4-8$$

Subtract 8 from -4 to get -12.

$$6x=-12$$

Divide both sides by 6.

$$x=\frac{-12}{6}$$

Divide -12 by 6 to get -2.

$$x=-2$$

Consider the first equation. Insert the known values of variables into the equation.

$$\frac{-2-1}{2}-\frac{y-1}{3}=-\frac{13}{36}$$

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

$$18\left(-2-1\right)-12\left(y-1\right)=-13$$

Subtract 1 from -2 to get -3.

$$18\left(-3\right)-12\left(y-1\right)=-13$$

Multiply 18 and -3 to get -54.

$$-54-12\left(y-1\right)=-13$$

Use the distributive property to multiply -12 by y-1.

$$-54-12y+12=-13$$

Add -54 and 12 to get -42.

$$-42-12y=-13$$

Add 42 to both sides.

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

Add -13 and 42 to get 29.

$$-12y=29$$

Divide both sides by -12.

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

The system is now solved.

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