Math Problem Solver

The system of linear equations has exactly one solution.

\[x = - \frac{3}{2}\]

\[y = \frac{7}{2}\]

Solve \(12 x + 9 y = 7 x + 6 y + 3\) for \(x\). \[x = \frac{3}{5} - \frac{3 y}{5}\]

Substitute \(\frac{3}{5} - \frac{3 y}{5}\) for \(x\) in \(7 x + 6 y + 3 = 4 x + 5 y + 2\) and simplify. $$\begin{aligned}7 x + 6 y + 3 &= 4 x + 5 y + 2 \\ 7 \left(\frac{3}{5} - \frac{3 y}{5}\right) + 6 y + 3 &= 4 \left(\frac{3}{5} - \frac{3 y}{5}\right) + 5 y + 2 \\ y &= \frac{7}{2} \end{aligned}$$

Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{3}{5} - \frac{3 y}{5} \\ x &= - \frac{3 \cdot 7}{2 \cdot 5} + \frac{3}{5} \\ x &= - \frac{3}{2}\end{aligned}$$