Solve {l}{2/x-3/y=15}{8/4-5/y=77}

$$\left. \begin{array} { l } { \frac { 2 } { x } - \frac { 3 } { y } = 15 } \\ { \frac { 8 } { 4 } - \frac { 5 } { y } = 77 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{1}{15}\approx -0.066666667$$

$$y=-\frac{1}{15}\approx -0.066666667$$

Solution Steps

Consider the second equation. Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4y, the least common multiple of 4,y.

$$y\times 8-4\times 5=308y$$

Multiply -4 and 5 to get -20.

$$y\times 8-20=308y$$

Subtract 308y from both sides.

$$y\times 8-20-308y=0$$

Combine y\times 8 and -308y to get -300y.

$$-300y-20=0$$

Add 20 to both sides. Anything plus zero gives itself.

$$-300y=20$$

Divide both sides by -300.

$$y=\frac{20}{-300}$$

Reduce the fraction \frac{20}{-300} to lowest terms by extracting and canceling out 20.

$$y=-\frac{1}{15}$$

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

$$\frac{2}{x}-\frac{3}{-\frac{1}{15}}=15$$

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

$$2-x\times \frac{3}{-\frac{1}{15}}=15x$$

Divide 3 by -\frac{1}{15} by multiplying 3 by the reciprocal of -\frac{1}{15}.

$$2-x\times 3\left(-15\right)=15x$$

Multiply 3 and -15 to get -45.

$$2-x\left(-45\right)=15x$$

Subtract 15x from both sides.

$$2-x\left(-45\right)-15x=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-x\left(-45\right)-15x=-2$$

Multiply -1 and -45 to get 45.

$$45x-15x=-2$$

Combine 45x and -15x to get 30x.

$$30x=-2$$

Divide both sides by 30.

$$x=\frac{-2}{30}$$

Reduce the fraction \frac{-2}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{15}$$

The system is now solved.

$$x=-\frac{1}{15} y=-\frac{1}{15}$$