x+y=25
x-y=5
x=?
You asked:
Given the following equations: \[\begin{aligned}x + y &= 25\\ x - y &= 5\end{aligned}\] Evaluate \(x\).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitution is \( x = 15 \).
\[x = 15\]
Solve \(x + y = 25\) for \(x\). \[x = 25 - y\]
Substitute \(25 - y\) for \(x\) in \(x - y = 5\) and simplify. $$\begin{aligned}x - y &= 5 \\ \left(25 - y\right) - y &= 5 \\ y &= 10 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 25 - y \\ x &= 25 - 10 \\ x &= 15\end{aligned}$$