x+y=12 ,x-y =2 then find xy?
You asked:
Given the following equations: \[\begin{aligned}x + y &= 12\\ x - y &= 2\end{aligned}\] Evaluate \(x y\).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = 7 \), \( y = 5 \).
\[x y = 35\]
Solve \(x + y = 12\) for \(x\). \[x = 12 - y\]
Substitute \(12 - y\) for \(x\) in \(x - y = 2\) and simplify. $$\begin{aligned}x - y &= 2 \\ \left(12 - y\right) - y &= 2 \\ y &= 5 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 12 - y \\ x &= 12 - 5 \\ x &= 7\end{aligned}$$
By substituting these values into the expression, we find that:$$\begin{aligned} x y &= 7 \cdot 5\\ &=35\end{aligned}$$