Solve {l}{5/2+x/5=-4}{y/3+x/6=frac{1}{6}}

$$\left\{ \begin{array} { l } { \frac { 5 } { 2 } + \frac { x } { 5 } = - 4 } \\ { \frac { y } { 3 } + \frac { x } { 6 } = \frac { 1 } { 6 } } \end{array} \right.$$

Solve for x, y

$$x = -\frac{65}{2} = -32\frac{1}{2} = -32.5$$

$$y = \frac{67}{4} = 16\frac{3}{4} = 16.75$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 10, the least common multiple of 2,5.

$$25+2x=-40$$

Subtract 25 from both sides.

$$2x=-40-25$$

Subtract 25 from -40 to get -65.

$$2x=-65$$

Divide both sides by 2.

$$x=-\frac{65}{2}$$

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

$$\frac{y}{3}+\frac{-\frac{65}{2}}{6}=\frac{1}{6}$$

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

$$2y-\frac{65}{2}=1$$

Add \frac{65}{2} to both sides.

$$2y=1+\frac{65}{2}$$

Add 1 and \frac{65}{2} to get \frac{67}{2}.

$$2y=\frac{67}{2}$$

Divide both sides by 2.

$$y=\frac{\frac{67}{2}}{2}$$

Express \frac{\frac{67}{2}}{2} as a single fraction.

$$y=\frac{67}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$y=\frac{67}{4}$$

The system is now solved.

$$x=-\frac{65}{2} y=\frac{67}{4}$$