if a+b =25 and a-b=15 then (A+B+C)=?
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MathBot Answer:
Assuming \(A\) and \(a\) are referring to the same variable.
Assuming \(B\) and \(b\) are referring to the same variable.
The system of linear equations has exactly one solution.
The substitutions are \( a = 20 \), \( b = 5 \).
\[A + B + C = C + 25\]
Solve \(a + b = 25\) for \(a\). \[a = 25 - b\]
Substitute \(25 - b\) for \(a\) in \(a - b = 15\) and simplify. $$\begin{aligned}a - b &= 15 \\ \left(25 - b\right) - b &= 15 \\ b &= 5 \end{aligned}$$
Use substitution of the numerical value of \(b\) to get the values of \(a\). $$\begin{aligned}a &= 25 - b \\ a &= 25 - 5 \\ a &= 20\end{aligned}$$
By substituting these values into the expression, we find that:$$\begin{aligned} A + B + C &= C + 5 + 20\\ &=C + 25\end{aligned}$$