7m+12h=8896
4m+15h=8634
find value of m and h
You asked:
Given \( 7 m + 12 h = 8896 \), \( 4 m + 15 h = 8634 \), evaluate \( m \), \( h \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[m = \frac{9944}{19}\]
\[h = \frac{24854}{57}\]
Solve \(12 h + 7 m = 8896\) for \(h\). \[h = \frac{2224}{3} - \frac{7 m}{12}\]
Substitute \(\frac{2224}{3} - \frac{7 m}{12}\) for \(h\) in \(15 h + 4 m = 8634\) and simplify. $$\begin{aligned}15 h + 4 m &= 8634 \\ 15 \left(\frac{2224}{3} - \frac{7 m}{12}\right) + 4 m &= 8634 \\ m &= \frac{9944}{19} \end{aligned}$$
Use substitution of the numerical value of \(m\) to get the values of \(h\). $$\begin{aligned}h &= \frac{2224}{3} - \frac{7 m}{12} \\ h &= - \frac{7 \cdot 9944}{12 \cdot 19} + \frac{2224}{3} \\ h &= \frac{24854}{57}\end{aligned}$$