Solve {l}{3x+3y-144=2x+4y}{2x+3y-12=2x+4y}

$$\left\{ \begin{array} { l } { 3 x + 3 y - 144 = 2 x + 4 y } \\ { 2 x + 3 y - 12 = 2 x + 4 y } \end{array} \right.$$

Solve for x, y

$$x=132$$

$$y=-12$$

Solution Steps

Consider the first equation. Subtract 2x from both sides.

$$3x+3y-144-2x=4y$$

Combine 3x and -2x to get x.

$$x+3y-144=4y$$

Subtract 4y from both sides.

$$x+3y-144-4y=0$$

Combine 3y and -4y to get -y.

$$x-y-144=0$$

Add 144 to both sides. Anything plus zero gives itself.

$$x-y=144$$

Consider the second equation. Subtract 2x from both sides.

$$2x+3y-12-2x=4y$$

Combine 2x and -2x to get 0.

$$3y-12=4y$$

Subtract 4y from both sides.

$$3y-12-4y=0$$

Combine 3y and -4y to get -y.

$$-y-12=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$-y=12$$

Divide both sides by -1.

$$y=-12$$

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

$$x-\left(-12\right)=144$$

Multiply -1 and -12 to get 12.

$$x+12=144$$

Subtract 12 from both sides.

$$x=144-12$$

Subtract 12 from 144 to get 132.

$$x=132$$

The system is now solved.

$$x=132 y=-12$$