Solve {l}{1/9(2m-16)=1/3(2m+1)}{-4(r+2)=4(2-2r)}{12(5+2y)=4y-(6}

$$\left. \begin{array} { l } { \frac { 1 } { 9 } ( 2 m - 16 ) = \frac { 1 } { 3 } ( 2 m + 1 ) } \\ { - 4 ( r + 2 ) = 4 ( 2 - 2 r ) } \\ { 12 ( 5 + 2 y ) = 4 y - ( 6 } \end{array} \right.$$

Solve for m, r, y

$$y = -\frac{33}{10} = -3\frac{3}{10} = -3.3$$

$$r=4$$

$$m = -\frac{19}{4} = -4\frac{3}{4} = -4.75$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{1}{9} by 2m-16.

$$\frac{2}{9}m-\frac{16}{9}=\frac{1}{3}\left(2m+1\right)$$

Use the distributive property to multiply \frac{1}{3} by 2m+1.

$$\frac{2}{9}m-\frac{16}{9}=\frac{2}{3}m+\frac{1}{3}$$

Subtract \frac{2}{3}m from both sides.

$$\frac{2}{9}m-\frac{16}{9}-\frac{2}{3}m=\frac{1}{3}$$

Combine \frac{2}{9}m and -\frac{2}{3}m to get -\frac{4}{9}m.

$$-\frac{4}{9}m-\frac{16}{9}=\frac{1}{3}$$

Add \frac{16}{9} to both sides.

$$-\frac{4}{9}m=\frac{1}{3}+\frac{16}{9}$$

Add \frac{1}{3} and \frac{16}{9} to get \frac{19}{9}.

$$-\frac{4}{9}m=\frac{19}{9}$$

Multiply both sides by -\frac{9}{4}, the reciprocal of -\frac{4}{9}.

$$m=\frac{19}{9}\left(-\frac{9}{4}\right)$$

Multiply \frac{19}{9} and -\frac{9}{4} to get -\frac{19}{4}.

$$m=-\frac{19}{4}$$

Consider the second equation. Use the distributive property to multiply -4 by r+2.

$$-4r-8=4\left(2-2r\right)$$

Use the distributive property to multiply 4 by 2-2r.

$$-4r-8=8-8r$$

Add 8r to both sides.

$$-4r-8+8r=8$$

Combine -4r and 8r to get 4r.

$$4r-8=8$$

Add 8 to both sides.

$$4r=8+8$$

Add 8 and 8 to get 16.

$$4r=16$$

Divide both sides by 4.

$$r=\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$r=4$$

Consider the third equation. Use the distributive property to multiply 12 by 5+2y.

$$60+24y=4y-6$$

Subtract 4y from both sides.

$$60+24y-4y=-6$$

Combine 24y and -4y to get 20y.

$$60+20y=-6$$

Subtract 60 from both sides.

$$20y=-6-60$$

Subtract 60 from -6 to get -66.

$$20y=-66$$

Divide both sides by 20.

$$y=\frac{-66}{20}$$

Reduce the fraction \frac{-66}{20} to lowest terms by extracting and canceling out 2.

$$y=-\frac{33}{10}$$

The system is now solved.

$$m=-\frac{19}{4} r=4 y=-\frac{33}{10}$$