Solve {l}{2(6x-4)/4+3(y-1)/6=0}{3(2x-y)-(6x+3y)=6}

$$\left\{ \begin{array} { l } { \frac { 2 ( 6 x - 4 ) } { 4 } + \frac { 3 ( y - 1 ) } { 6 } = 0 } \\ { 3 ( 2 x - y ) - ( 6 x + 3 y ) = 6 } \end{array} \right.$$

Solve for x, y

$$x=1$$

$$y=-1$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 4,6.

$$3\times 2\left(6x-4\right)+2\times 3\left(y-1\right)=0$$

Multiply 3 and 2 to get 6.

$$6\left(6x-4\right)+2\times 3\left(y-1\right)=0$$

Use the distributive property to multiply 6 by 6x-4.

$$36x-24+2\times 3\left(y-1\right)=0$$

Multiply 2 and 3 to get 6.

$$36x-24+6\left(y-1\right)=0$$

Use the distributive property to multiply 6 by y-1.

$$36x-24+6y-6=0$$

Subtract 6 from -24 to get -30.

$$36x-30+6y=0$$

Add 30 to both sides. Anything plus zero gives itself.

$$36x+6y=30$$

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

$$6x-3y-\left(6x+3y\right)=6$$

To find the opposite of 6x+3y, find the opposite of each term.

$$6x-3y-6x-3y=6$$

Combine 6x and -6x to get 0.

$$-3y-3y=6$$

Combine -3y and -3y to get -6y.

$$-6y=6$$

Divide both sides by -6.

$$y=\frac{6}{-6}$$

Divide 6 by -6 to get -1.

$$y=-1$$

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

$$36x+6\left(-1\right)=30$$

Multiply 6 and -1 to get -6.

$$36x-6=30$$

Add 6 to both sides.

$$36x=30+6$$

Add 30 and 6 to get 36.

$$36x=36$$

Divide both sides by 36.

$$x=\frac{36}{36}$$

Divide 36 by 36 to get 1.

$$x=1$$

The system is now solved.

$$x=1 y=-1$$