Solve {l}{7c+3(3c+5)=-103}{-3n+3(4n+15)=-21}

$$\left. \begin{array} { l } { 7 c + 3 ( 3 c + 5 ) = - 103 } \\ { - 3 n + 3 ( 4 n + 15 ) = - 21 } \end{array} \right.$$

Solve for c, n

$$c = -\frac{59}{8} = -7\frac{3}{8} = -7.375$$

$$n = -\frac{22}{3} = -7\frac{1}{3} \approx -7.333333333$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 3 by 3c+5.

$$7c+9c+15=-103$$

Combine 7c and 9c to get 16c.

$$16c+15=-103$$

Subtract 15 from both sides.

$$16c=-103-15$$

Subtract 15 from -103 to get -118.

$$16c=-118$$

Divide both sides by 16.

$$c=\frac{-118}{16}$$

Reduce the fraction \frac{-118}{16} to lowest terms by extracting and canceling out 2.

$$c=-\frac{59}{8}$$

Consider the second equation. Use the distributive property to multiply 3 by 4n+15.

$$-3n+12n+45=-21$$

Combine -3n and 12n to get 9n.

$$9n+45=-21$$

Subtract 45 from both sides.

$$9n=-21-45$$

Subtract 45 from -21 to get -66.

$$9n=-66$$

Divide both sides by 9.

$$n=\frac{-66}{9}$$

Reduce the fraction \frac{-66}{9} to lowest terms by extracting and canceling out 3.

$$n=-\frac{22}{3}$$

The system is now solved.

$$c=-\frac{59}{8} n=-\frac{22}{3}$$