Solve {l}{2/x-3/y=1}{1/x+7/4=1}

$$\left. \begin{array} { l } { \frac { 2 } { x } - \frac { 3 } { y } = 1 } \\ { \frac { 1 } { x } + \frac { 7 } { 4 } = 1 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

$$y = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

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 4x, the least common multiple of x,4.

$$4+4x\times \frac{7}{4}=4x$$

Multiply 4 and \frac{7}{4} to get 7.

$$4+7x=4x$$

Subtract 4x from both sides.

$$4+7x-4x=0$$

Combine 7x and -4x to get 3x.

$$4+3x=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$3x=-4$$

Divide both sides by 3.

$$x=-\frac{4}{3}$$

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

$$\frac{2}{-\frac{4}{3}}-\frac{3}{y}=1$$

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

$$y\times \frac{2}{-\frac{4}{3}}-3=y$$

Divide 2 by -\frac{4}{3} by multiplying 2 by the reciprocal of -\frac{4}{3}.

$$y\times 2\left(-\frac{3}{4}\right)-3=y$$

Multiply 2 and -\frac{3}{4} to get -\frac{3}{2}.

$$y\left(-\frac{3}{2}\right)-3=y$$

Subtract y from both sides.

$$y\left(-\frac{3}{2}\right)-3-y=0$$

Combine y\left(-\frac{3}{2}\right) and -y to get -\frac{5}{2}y.

$$-\frac{5}{2}y-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$-\frac{5}{2}y=3$$

Multiply both sides by -\frac{2}{5}, the reciprocal of -\frac{5}{2}.

$$y=3\left(-\frac{2}{5}\right)$$

Multiply 3 and -\frac{2}{5} to get -\frac{6}{5}.

$$y=-\frac{6}{5}$$

The system is now solved.

$$x=-\frac{4}{3} y=-\frac{6}{5}$$