solve 9b + 9c + 7d + 10e + 26f + 13g = 600, 15a + 9c + 2e + 13g = 900, 15e + 8f = 400, 21a + 13b + 9c + 7d + 13g = 1200
You asked:
Solve the system of equations:\[\begin{aligned}9 b + 9 c + 7 d + 10 e + 26 f + 13 g &= 600\\15 a + 9 c + 2 e + 13 g &= 900\\15 e + 8 f &= 400\\21 a + 13 b + 9 c + 7 d + 13 g &= 1200\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}a &= \frac{28 d}{249} - \frac{2047 e}{996} + \frac{23500}{249}\\b &= - \frac{49 d}{83} - \frac{1700}{83} + \frac{183 e}{166}\\c &= - \frac{140 d}{747} - \frac{13 g}{9} - \frac{42800}{747} + \frac{9571 e}{2988}\\f &= 50 - \frac{15 e}{8}\end{aligned}$$
\(d\) is a free variable.
\(g\) is a free variable.