When solving the system \( \begin{cases} 2x + y = 50 \\ 4x - 5y = 30 \end{cases} \) we obtain that \( 5(x + y) \) equals:
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50
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100
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200
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150
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300
Try to solve it before checking the answer.
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150
Multiplying the first equation by -2 and adding the result to the second equation, we obtain:
\[ -7y = -70 \Rightarrow y = 10 \]Replacing \( y = 10 \) in the first equation:
\[ \begin{aligned} 2x + 10 = 50 &\Rightarrow 2x = 40 \\[2em] &\Rightarrow x = 20 \end{aligned} \]Now, we have:
\[ \begin{aligned} 5(x + y) &= 5(20 + 10) \\[2em] &= 5(30) = \boldsymbol{150} \end{aligned} \]