Solve {l}{3x-6=7}{3y-6=x}

$$\left. \begin{array} { l } { 3 x - 6 = 7 } \\ { 3 y - 6 = x } \end{array} \right.$$

Solve for x, y

$$x = \frac{13}{3} = 4\frac{1}{3} \approx 4.333333333$$

$$y = \frac{31}{9} = 3\frac{4}{9} \approx 3.444444444$$

Solution Steps

Consider the first equation. Add 6 to both sides.

$$3x=7+6$$

Add 7 and 6 to get 13.

$$3x=13$$

Divide both sides by 3.

$$x=\frac{13}{3}$$

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

$$3y-6=\frac{13}{3}$$

Add 6 to both sides.

$$3y=\frac{13}{3}+6$$

Add \frac{13}{3} and 6 to get \frac{31}{3}.

$$3y=\frac{31}{3}$$

Divide both sides by 3.

$$y=\frac{\frac{31}{3}}{3}$$

Express \frac{\frac{31}{3}}{3} as a single fraction.

$$y=\frac{31}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$y=\frac{31}{9}$$

The system is now solved.

$$x=\frac{13}{3} y=\frac{31}{9}$$