Let's solve the system of equations:
[tex]$
\begin{aligned}
1.\quad 2.5y + 3x &= 27 \\
2.\quad 5x - 2.5y &= 5
\end{aligned}
$[/tex]
We want to find the result of adding these two equations.
First, let's write both equations in a more convenient form:
[tex]$
\begin{aligned}
1.\quad 2.5y + 3x &= 27 \\
2.\quad 5x - 2.5y &= 5
\end{aligned}
$[/tex]
When we add these two equations together, we sum both left-hand sides and both right-hand sides:
[tex]$
(2.5y + 3x) + (5x - 2.5y) = 27 + 5
$[/tex]
Simplify the left-hand side:
[tex]$
2.5y + 5x - 2.5y + 3x = 8x
$[/tex]
Combine like terms:
[tex]$
8x = 32
$[/tex]
This equation represents the result of adding the two given equations together. Therefore, the correct result is:
[tex]$
8x - 32 = 0
$[/tex]
