Solve {l}{1/x+1/3y=2}{1/2+1/2y=frac{73}{6}}

$$\left. \begin{array} { l } { \frac { 1 } { x } + \frac { 1 } { 3 y } = 2 } \\ { \frac { 1 } { 2 } + \frac { 1 } { 2 y } = \frac { 73 } { 6 } } \end{array} \right.$$

Solve for x, y

$$x=-\frac{9}{52}\approx -0.173076923$$

$$y=\frac{3}{70}\approx 0.042857143$$

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 6y, the least common multiple of 2,2y,6.

$$6y\times \frac{1}{2}+3=73y$$

Multiply 6 and \frac{1}{2} to get 3.

$$3y+3=73y$$

Subtract 73y from both sides.

$$3y+3-73y=0$$

Combine 3y and -73y to get -70y.

$$-70y+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-70y=-3$$

Divide both sides by -70.

$$y=\frac{-3}{-70}$$

Fraction \frac{-3}{-70} can be simplified to \frac{3}{70} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{3}{70}$$

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

$$\frac{1}{x}+\frac{1}{3\times \frac{3}{70}}=2$$

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

$$1+\frac{70}{9}x=2x$$

Subtract 2x from both sides.

$$1+\frac{70}{9}x-2x=0$$

Combine \frac{70}{9}x and -2x to get \frac{52}{9}x.

$$1+\frac{52}{9}x=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$\frac{52}{9}x=-1$$

Multiply both sides by \frac{9}{52}, the reciprocal of \frac{52}{9}.

$$x=-\frac{9}{52}$$

The system is now solved.

$$x=-\frac{9}{52} y=\frac{3}{70}$$