Solve {l}{-2n+2(3n+14)=-20}{-5a-2(-7a-10)=128}

$$\left. \begin{array} { l } { - 2 n + 2 ( 3 n + 14 ) = - 20 } \\ { - 5 a - 2 ( - 7 a - 10 ) = 128 } \end{array} \right.$$

Solve for n, a

$$n=-12$$

$$a=12$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by 3n+14.

$$-2n+6n+28=-20$$

Combine -2n and 6n to get 4n.

$$4n+28=-20$$

Subtract 28 from both sides.

$$4n=-20-28$$

Subtract 28 from -20 to get -48.

$$4n=-48$$

Divide both sides by 4.

$$n=\frac{-48}{4}$$

Divide -48 by 4 to get -12.

$$n=-12$$

Consider the second equation. Use the distributive property to multiply -2 by -7a-10.

$$-5a+14a+20=128$$

Combine -5a and 14a to get 9a.

$$9a+20=128$$

Subtract 20 from both sides.

$$9a=128-20$$

Subtract 20 from 128 to get 108.

$$9a=108$$

Divide both sides by 9.

$$a=\frac{108}{9}$$

Divide 108 by 9 to get 12.

$$a=12$$

The system is now solved.

$$n=-12 a=12$$