Exercise 57

When solving the system   \( \begin{cases} 2x + y = 50 \\ 4x - 5y = 30 \end{cases} \)   we obtain that \( 5(x + y) \) equals:

  1. 50

  2. 100

  3. 200

  4. 150

  5. 300

Try to solve it before checking the answer.
  1. 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:

\[ \begin{aligned} 5(x + y) &= 5(20 + 10) \\[2em] &= 5(30) = \boldsymbol{150} \end{aligned} \]