Math Problem Solver

The system of equations has one solution.

\[a = \frac{1}{42}, b = 2\]

Solve \(9 a b + 6 a = \frac{4}{7}\) for \(a\). \[a = \frac{4}{21 \cdot \left(3 b + 2\right)}\]Substitute \(\frac{4}{21 \cdot \left(3 b + 2\right)}\) for \(a\) in \(12 a b + 18 a = 1\) and simplify. $$\begin{aligned}12 a b + 18 a &= 1 \\ 12 \left(\frac{4}{21 \cdot \left(3 b + 2\right)}\right) b + 18 \left(\frac{4}{21 \cdot \left(3 b + 2\right)}\right) &= 1 \\ \frac{8 \cdot \left(2 b + 3\right)}{7 \cdot \left(3 b + 2\right)} &= 1 \end{aligned}$$Substitute \(2\) into \(9 a b + 6 a = \frac{4}{7}\) to solve for \(a\). \[\begin{aligned}24 a &= \frac{4}{7}\\a &= \frac{1}{42}\end{aligned}\]This yields the following solution. $$\begin{aligned}a = \frac{1}{42},\,b = 2\end{aligned}$$