Solve {l}{8/x+11/y=13}{5/x+7/x=12}

$$\left. \begin{array} { l } { \frac { 8 } { x } + \frac { 11 } { y } = 13 } \\ { \frac { 5 } { x } + \frac { 7 } { x } = 12 } \end{array} \right.$$

Solve for x, y

$$x=1$$

$$y = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

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 x.

$$5+7=12x$$

Add 5 and 7 to get 12.

$$12=12x$$

Swap sides so that all variable terms are on the left hand side.

$$12x=12$$

Divide both sides by 12.

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

Divide 12 by 12 to get 1.

$$x=1$$

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

$$\frac{8}{1}+\frac{11}{y}=13$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$y\times 8+11=13y$$

Subtract 13y from both sides.

$$y\times 8+11-13y=0$$

Combine y\times 8 and -13y to get -5y.

$$-5y+11=0$$

Subtract 11 from both sides. Anything subtracted from zero gives its negation.

$$-5y=-11$$

Divide both sides by -5.

$$y=\frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{11}{5}$$

The system is now solved.

$$x=1 y=\frac{11}{5}$$