find 4AB when A+B =15 and A-B =3?
You asked:
Given the following equations: \[\begin{aligned}A + B &= 15\\ A - B &= 3\end{aligned}\] Evaluate \(4 A B\).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( A = 9 \), \( B = 6 \).
\[4 A B = 216\]
Solve \(A + B = 15\) for \(A\). \[A = 15 - B\]
Substitute \(15 - B\) for \(A\) in \(A - B = 3\) and simplify. $$\begin{aligned}A - B &= 3 \\ \left(15 - B\right) - B &= 3 \\ B &= 6 \end{aligned}$$
Use substitution of the numerical value of \(B\) to get the values of \(A\). $$\begin{aligned}A &= 15 - B \\ A &= 15 - 6 \\ A &= 9\end{aligned}$$
By substituting these values into the expression, we find that:$$\begin{aligned} 4 A B &= 4 \cdot 9 \cdot 6\\ &=216\end{aligned}$$