Solve {l}{3x+2(y-3)=2y}{2x-(y+2x)=4}

$$\left\{ \begin{array} { l } { 3 x + 2 ( y - 3 ) = 2 y } \\ { 2 x - ( y + 2 x ) = 4 } \end{array} \right.$$

Solve for x, y

$$x=2$$

$$y=-4$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by y-3.

$$3x+2y-6=2y$$

Subtract 2y from both sides.

$$3x+2y-6-2y=0$$

Combine 2y and -2y to get 0.

$$3x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$3x=6$$

Divide both sides by 3.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$

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

$$2\times 2-\left(y+2\times 2\right)=4$$

Multiply 2 and 2 to get 4.

$$4-\left(y+2\times 2\right)=4$$

Multiply 2 and 2 to get 4.

$$4-\left(y+4\right)=4$$

To find the opposite of y+4, find the opposite of each term.

$$4-y-4=4$$

Subtract 4 from 4 to get 0.

$$-y=4$$

Divide both sides by -1.

$$y=-4$$

The system is now solved.

$$x=2 y=-4$$