Find the value of x when:
2x + y = 13 and x − y = 2
You asked:
Given the following equations: \[\begin{aligned}2 x + y &= 13\\ x - y &= 2\end{aligned}\] Evaluate \(x\).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = 5\]
Solve \(2 x + y = 13\) for \(x\). \[x = \frac{13}{2} - \frac{y}{2}\]
Substitute \(\frac{13}{2} - \frac{y}{2}\) for \(x\) in \(x - y = 2\) and simplify. $$\begin{aligned}x - y &= 2 \\ \left(\frac{13}{2} - \frac{y}{2}\right) - y &= 2 \\ y &= 3 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{13}{2} - \frac{y}{2} \\ x &= - \frac{3}{2} + \frac{13}{2} \\ x &= 5\end{aligned}$$