Solve {r}{a_{y}+12y=129}{-16y-12y=-144}

$$\left. \begin{array} { r } { a _ { y } + 12 y = 129 } \\ { - 16 y - 12 y = - 144 } \end{array} \right.$$

Solve for a_y, y

$$y = \frac{36}{7} = 5\frac{1}{7} \approx 5.142857143$$

$$a_{y} = \frac{471}{7} = 67\frac{2}{7} \approx 67.285714286$$

Solution Steps

Consider the second equation. Combine -16y and -12y to get -28y.

$$-28y=-144$$

Divide both sides by -28.

$$y=\frac{-144}{-28}$$

Reduce the fraction \frac{-144}{-28} to lowest terms by extracting and canceling out -4.

$$y=\frac{36}{7}$$

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

$$a_{y}+12\times \frac{36}{7}=129$$

Multiply 12 and \frac{36}{7} to get \frac{432}{7}.

$$a_{y}+\frac{432}{7}=129$$

Subtract \frac{432}{7} from both sides.

$$a_{y}=129-\frac{432}{7}$$

Subtract \frac{432}{7} from 129 to get \frac{471}{7}.

$$a_{y}=\frac{471}{7}$$

The system is now solved.

$$a_{y}=\frac{471}{7} y=\frac{36}{7}$$