Solve {l}{x/2+1/3=2}{3x-2(2)y=2}

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

Solve for x, y

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$y=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3x+2=12$$

Subtract 2 from both sides.

$$3x=12-2$$

Subtract 2 from 12 to get 10.

$$3x=10$$

Divide both sides by 3.

$$x=\frac{10}{3}$$

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

$$3\times \frac{10}{3}-2\times 2y=2$$

Multiply 3 and \frac{10}{3} to get 10.

$$10-2\times 2y=2$$

Multiply 2 and 2 to get 4.

$$10-4y=2$$

Subtract 10 from both sides.

$$-4y=2-10$$

Subtract 10 from 2 to get -8.

$$-4y=-8$$

Divide both sides by -4.

$$y=\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$y=2$$

The system is now solved.

$$x=\frac{10}{3} y=2$$