Solve {l}{x/x+y=15}{1/x+2/5=1/24}

$$\left. \begin{array} { l } { \frac { x } { x } + y = 15 } \\ { \frac { 1 } { x } + \frac { 2 } { 5 } = \frac { 1 } { 24 } } \end{array} \right.$$

Solve for x, y

$$x = -\frac{120}{43} = -2\frac{34}{43} \approx -2.790697674$$

$$y=14$$

Solution Steps

Consider the second equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 120x, the least common multiple of x,5,24.

$$120+120x\times \frac{2}{5}=5x$$

Multiply 120 and \frac{2}{5} to get 48.

$$120+48x=5x$$

Subtract 5x from both sides.

$$120+48x-5x=0$$

Combine 48x and -5x to get 43x.

$$120+43x=0$$

Subtract 120 from both sides. Anything subtracted from zero gives its negation.

$$43x=-120$$

Divide both sides by 43.

$$x=-\frac{120}{43}$$

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

$$\frac{-\frac{120}{43}}{-\frac{120}{43}}+y=15$$

Divide -\frac{120}{43} by -\frac{120}{43} to get 1.

$$1+y=15$$

Subtract 1 from both sides.

$$y=15-1$$

Subtract 1 from 15 to get 14.

$$y=14$$

The system is now solved.

$$x=-\frac{120}{43} y=14$$