what's x if 2x = y and x + y = 65?
You asked:
Given the following equations: \[\begin{aligned}2 x &= y\\ x + y &= 65\end{aligned}\] Evaluate \(x\).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = \frac{65}{3}\]
Solve \(2 x = y\) for \(x\). \[x = \frac{y}{2}\]
Substitute \(\frac{y}{2}\) for \(x\) in \(x + y = 65\) and simplify. $$\begin{aligned}x + y &= 65 \\ \left(\frac{y}{2}\right) + y &= 65 \\ y &= \frac{130}{3} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{y}{2} \\ x &= \frac{130}{2 \cdot 3} \\ x &= \frac{65}{3}\end{aligned}$$