x+y=2
x-y=1
find x and y
You asked:
Given \( x + y = 2 \), \( x - y = 1 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = \frac{3}{2}\]
\[y = \frac{1}{2}\]
Solve \(x + y = 2\) for \(x\). \[x = 2 - y\]
Substitute \(2 - y\) for \(x\) in \(x - y = 1\) and simplify. $$\begin{aligned}x - y &= 1 \\ \left(2 - y\right) - y &= 1 \\ y &= \frac{1}{2} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 2 - y \\ x &= 2 - 1 \cdot \frac{1}{2} \\ x &= \frac{3}{2}\end{aligned}$$