2m+3n=12
m+n=5
find value of m and n
You asked:
Given \( 2 m + 3 n = 12 \), \( m + n = 5 \), evaluate \( m \), \( n \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[m = 3\]
\[n = 2\]
Solve \(2 m + 3 n = 12\) for \(m\). \[m = 6 - \frac{3 n}{2}\]
Substitute \(6 - \frac{3 n}{2}\) for \(m\) in \(m + n = 5\) and simplify. $$\begin{aligned}m + n &= 5 \\ \left(6 - \frac{3 n}{2}\right) + n &= 5 \\ n &= 2 \end{aligned}$$
Use substitution of the numerical value of \(n\) to get the values of \(m\). $$\begin{aligned}m &= 6 - \frac{3 n}{2} \\ m &= 6 - 3 \cdot 2 \cdot \frac{1}{2} \\ m &= 3\end{aligned}$$