solve for c given -3c + 4d = 3 and -4c -3d = 0
You asked:
Given the following equations: \[\begin{aligned}-\left( 3 c \right) + 4 d &= 3\\ -\left( 4 c \right) - 3 d &= 0\end{aligned}\] Evaluate \(c\).
MathBot Answer:
The system of linear equations has exactly one solution.
\[c = - \frac{9}{25}\]
Solve \(- 3 c + 4 d = 3\) for \(c\). \[c = \frac{4 d}{3} - 1\]
Substitute \(\frac{4 d}{3} - 1\) for \(c\) in \(- 4 c - 3 d = 0\) and simplify. $$\begin{aligned}- 4 c - 3 d &= 0 \\ - 4 \left(\frac{4 d}{3} - 1\right) - 3 d &= 0 \\ d &= \frac{12}{25} \end{aligned}$$
Use substitution of the numerical value of \(d\) to get the values of \(c\). $$\begin{aligned}c &= \frac{4 d}{3} - 1 \\ c &= \left(-1\right) 1 + 4 \cdot 12 \cdot \frac{1}{25} \cdot \frac{1}{3} \\ c &= - \frac{9}{25}\end{aligned}$$