Solve {l}{x-1/y-6*-2/3=-1}{x-5/2=-2/3}

$$\left. \begin{array} { l } { \frac { x - 1 } { y - 6 } \cdot - \frac { 2 } { 3 } = - 1 } \\ { \frac { x - 5 } { 2 } = - \frac { 2 } { 3 } } \end{array} \right.$$

Solve for x, y

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

$$y = \frac{70}{9} = 7\frac{7}{9} \approx 7.777777778$$

Solution Steps

Consider the second equation. Multiply both sides by 2.

$$x-5=-\frac{2}{3}\times 2$$

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

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

Add 5 to both sides.

$$x=-\frac{4}{3}+5$$

Add -\frac{4}{3} and 5 to get \frac{11}{3}.

$$x=\frac{11}{3}$$

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

$$\frac{\frac{11}{3}-1}{y-6}\left(-\frac{2}{3}\right)=-1$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$\frac{\frac{11}{3}-1}{y-6}=-\left(-\frac{3}{2}\right)$$

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

$$\frac{\frac{11}{3}-1}{y-6}=\frac{3}{2}$$

Variable y cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by 2\left(y-6\right), the least common multiple of y-6,2.

$$2\left(\frac{11}{3}-1\right)=3\left(y-6\right)$$

Subtract 1 from \frac{11}{3} to get \frac{8}{3}.

$$2\times \frac{8}{3}=3\left(y-6\right)$$

Multiply 2 and \frac{8}{3} to get \frac{16}{3}.

$$\frac{16}{3}=3\left(y-6\right)$$

Use the distributive property to multiply 3 by y-6.

$$\frac{16}{3}=3y-18$$

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

$$3y-18=\frac{16}{3}$$

Add 18 to both sides.

$$3y=\frac{16}{3}+18$$

Add \frac{16}{3} and 18 to get \frac{70}{3}.

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

Divide both sides by 3.

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

Express \frac{\frac{70}{3}}{3} as a single fraction.

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

Multiply 3 and 3 to get 9.

$$y=\frac{70}{9}$$

The system is now solved.

$$x=\frac{11}{3} y=\frac{70}{9}$$