Solve {l}{3x-2y=3x+3}{3y+2x=3y+2}

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

Solve for x, y

$$x=1$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Solution Steps

Consider the first equation. Subtract 3x from both sides.

$$3x-2y-3x=3$$

Combine 3x and -3x to get 0.

$$-2y=3$$

Divide both sides by -2.

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

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

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

Multiply 3 and -\frac{3}{2} to get -\frac{9}{2}.

$$-\frac{9}{2}+2x=3\left(-\frac{3}{2}\right)+2$$

Multiply 3 and -\frac{3}{2} to get -\frac{9}{2}.

$$-\frac{9}{2}+2x=-\frac{9}{2}+2$$

Add -\frac{9}{2} and 2 to get -\frac{5}{2}.

$$-\frac{9}{2}+2x=-\frac{5}{2}$$

Add \frac{9}{2} to both sides.

$$2x=-\frac{5}{2}+\frac{9}{2}$$

Add -\frac{5}{2} and \frac{9}{2} to get 2.

$$2x=2$$

Divide both sides by 2.

$$x=\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$x=1$$

The system is now solved.

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