If \(\frac{1}{2}\)x + 2y = 3 and \(\frac{3}{2}\)x and \(\frac{3}{2}\)x - 2y = 1, find (x + y)
Answer Details
Given the equations:
\begin{align*}
\frac{1}{2}x + 2y &= 3 \\
\frac{3}{2}x - 2y &= 1 \\
\end{align*}
We can solve for x and y using simultaneous equations:
First, multiply the first equation by 2:
\begin{align*}
x + 4y &= 6 \\
\frac{3}{2}x - 2y &= 1 \\
\end{align*}
Then, multiply the second equation by 2:
\begin{align*}
x + 4y &= 6 \\
3x - 4y &= 2 \\
\end{align*}
Add the equations together:
\begin{align*}
4x &= 8 \\
x &= 2 \\
\end{align*}
Substitute x = 2 back into the first equation:
\begin{align*}
\frac{1}{2}(2) + 2y &= 3 \\
1 + 2y &= 3 \\
2y &= 2 \\
y &= 1 \\
\end{align*}
Finally, substitute x = 2 and y = 1 into (x + y):
\begin{align*}
x + y &= 2 + 1 \\
&= 3 \\
\end{align*}
Therefore, (x + y) = 3, and the answer is.