Solve {l}{x-y/3-x+y/2=1}{x=-2}

$$\left. \begin{array} { l } { \frac { x - y } { 3 } - \frac { x + y } { 2 } = 1 } \\ { x = - 2 } \end{array} \right.$$

Solve for x, y

$$x=-2$$

$$y=-\frac{4}{5}=-0.8$$

Solution Steps

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

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

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

$$2\left(-2-y\right)-3\left(-2+y\right)=6$$

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

$$-4-2y-3\left(-2+y\right)=6$$

Use the distributive property to multiply -3 by -2+y.

$$-4-2y+6-3y=6$$

Add -4 and 6 to get 2.

$$2-2y-3y=6$$

Combine -2y and -3y to get -5y.

$$2-5y=6$$

Subtract 2 from both sides.

$$-5y=6-2$$

Subtract 2 from 6 to get 4.

$$-5y=4$$

Divide both sides by -5.

$$y=-\frac{4}{5}$$

The system is now solved.

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