Solve {l}{39*{(frac{99*{(13)}+1}{13})}=3900-y}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 39 \cdot {(\frac{99 \cdot {(13)} + 1}{13})} = 3900 - y }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, z, a

$$a=36$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 13.

$$39\left(99\times 13+1\right)=50700-13y$$

Multiply 99 and 13 to get 1287.

$$39\left(1287+1\right)=50700-13y$$

Add 1287 and 1 to get 1288.

$$39\times 1288=50700-13y$$

Multiply 39 and 1288 to get 50232.

$$50232=50700-13y$$

Swap sides so that all variable terms are on the left hand side.

$$50700-13y=50232$$

Subtract 50700 from both sides.

$$-13y=50232-50700$$

Subtract 50700 from 50232 to get -468.

$$-13y=-468$$

Divide both sides by -13.

$$y=\frac{-468}{-13}$$

Divide -468 by -13 to get 36.

$$y=36$$

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

$$z=36$$

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

$$a=36$$

The system is now solved.

$$y=36 z=36 a=36$$