Re: 2x+5y=14 and x+3y=20
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05 Oct 2025, 02:19
Given the system of equations:
$$
\(\begin{gathered}
2 x+5 y=14 \\
x+3 y=20
\end{gathered}\)
$$
First, multiply the second equation by 2 to align the coefficients of $x$ :
$$
\(2(x+3 y)=2 \times 20 \Longrightarrow 2 x+6 y=40\)
$$
Now subtract the first equation from this:
$$
\(\begin{gathered}
(2 x+6 y)-(2 x+5 y)=40-14 \\
2 x+6 y-2 x-5 y=26 \\
y=26
\end{gathered}\)
$$
Substitute $y=26$ into the second original equation:
$$
\(\begin{gathered}
x+3(26)=20 \\
x+78=20 \\
x=20-78=-58
\end{gathered}\)
$$
Calculate $x+y$ :
$$
\(x+y=-58+26=-32\)
$$
Comparison:
- Quantity A: $\(x+y=-32\)$
- Quantity B : \(-32\)
They are equal.
Final answer:
The two quantities are equal.