Math Problem Solver

The system of linear equations has exactly one solution.

The substitutions are \( a = -1 \), \( c = \frac{3}{2} \).

\[a = -1\]

\[c = \frac{3}{2}\]

Solve \(3 a + 4 c = 3\) for \(a\). \[a = 1 - \frac{4 c}{3}\]

Substitute \(1 - \frac{4 c}{3}\) for \(a\) in \(a + 2 c = 2\) and simplify. $$\begin{aligned}a + 2 c &= 2 \\ \left(1 - \frac{4 c}{3}\right) + 2 c &= 2 \\ c &= \frac{3}{2} \end{aligned}$$

Use substitution of the numerical value of \(c\) to get the values of \(a\). $$\begin{aligned}a &= 1 - \frac{4 c}{3} \\ a &= 1 - \fra\frac{3}{2}{4 \\frac{3}{2}dot \frac{3}{2}}{3} \\ a &= -1\end{aligned}$$