Solve {l}{2(y+3)=21-3y}{(2-c)+3(c-3)=-13}{-3(1-3b)-12=12}

$$\left. \begin{array} { l } { 2 ( y + 3 ) = 21 - 3 y } \\ { ( 2 - c ) + 3 ( c - 3 ) = - 13 } \\ { - 3 ( 1 - 3 b ) - 12 = 12 } \end{array} \right.$$

Solve for y, c, b

$$y=3$$

$$c=-3$$

$$b=3$$

Solution Steps

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

$$2y+6=21-3y$$

Add 3y to both sides.

$$2y+6+3y=21$$

Combine 2y and 3y to get 5y.

$$5y+6=21$$

Subtract 6 from both sides.

$$5y=21-6$$

Subtract 6 from 21 to get 15.

$$5y=15$$

Divide both sides by 5.

$$y=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$y=3$$

Consider the second equation. Use the distributive property to multiply 3 by c-3.

$$2-c+3c-9=-13$$

Combine -c and 3c to get 2c.

$$2+2c-9=-13$$

Subtract 9 from 2 to get -7.

$$-7+2c=-13$$

Add 7 to both sides.

$$2c=-13+7$$

Add -13 and 7 to get -6.

$$2c=-6$$

Divide both sides by 2.

$$c=\frac{-6}{2}$$

Divide -6 by 2 to get -3.

$$c=-3$$

Consider the third equation. Use the distributive property to multiply -3 by 1-3b.

$$-3+9b-12=12$$

Subtract 12 from -3 to get -15.

$$-15+9b=12$$

Add 15 to both sides.

$$9b=12+15$$

Add 12 and 15 to get 27.

$$9b=27$$

Divide both sides by 9.

$$b=\frac{27}{9}$$

Divide 27 by 9 to get 3.

$$b=3$$

The system is now solved.

$$y=3 c=-3 b=3$$