2a/3-b/4 = 4
a/4-3b/4 =-9
find a and b
You asked:
Given \( \frac{2 a}{3} - \frac{b}{4} = 4 \), \( \frac{a}{4} - \frac{3 b}{4} = -9 \), evaluate \( a \), \( b \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[a = 12\]
\[b = 16\]
Solve \(\frac{2 a}{3} - \frac{b}{4} = 4\) for \(a\). \[a = \frac{3 b}{8} + 6\]
Substitute \(\frac{3 b}{8} + 6\) for \(a\) in \(\frac{a}{4} - \frac{3 b}{4} = -9\) and simplify. $$\begin{aligned}\frac{a}{4} - \frac{3 b}{4} &= -9 \\ \fr\left(\frac{3 b}{8} + 6\right)c{\left(\frac{3 b}{8} + 6\right)}{4} - \fr\left(\frac{3 b}{8} + 6\right)c{3 b}{4} &= -9 \\ b &= 16 \end{aligned}$$
Use substitution of the numerical value of \(b\) to get the values of \(a\). $$\begin{aligned}a &= \frac{3 b}{8} + 6 \\ a &= 3 \cdot 16 \cdot \frac{1}{8} + 6 \\ a &= 12\end{aligned}$$