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

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

Solve for x, y

$$x=2$$

$$y=5$$

Solution Steps

Consider the second equation. Subtract 3y from both sides.

$$3+2y-3y=-2$$

Combine 2y and -3y to get -y.

$$3-y=-2$$

Subtract 3 from both sides.

$$-y=-2-3$$

Subtract 3 from -2 to get -5.

$$-y=-5$$

Divide both sides by -1.

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

Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.

$$y=5$$

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

$$x+5=3+2x$$

Subtract 2x from both sides.

$$x+5-2x=3$$

Combine x and -2x to get -x.

$$-x+5=3$$

Subtract 5 from both sides.

$$-x=3-5$$

Subtract 5 from 3 to get -2.

$$-x=-2$$

Divide both sides by -1.

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

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x=2$$

The system is now solved.

$$x=2 y=5$$