Question

Find the value of x + y for the following equations: 2x + 7y = 9 and 7x + 2y = 27​

Answer 1

Answer:

$x = \frac{19}{5} \\ \\ \\ \\ y = \frac{1}{5}$

Step-by-step explanation:

$2x + 7y = 9 \\ \\ \\ \\ \\ 7x + 2y = 27 \\ \\ \\ \\ \\ \\ \\ adding \: equations \\ \\ \\ \\ \\ 9x + 9y = 36 \\ \\ x + y = 4 \\ \\ \\ \\ \\ subtracting \: \: \: original \: equations \\ \\ \\ \\ \\ \\ \\ 5x - 5y = 18 \\ \\ \\ x - y = \frac{18}{5} \\ \\ \\ \\ \\ therefore \: \: \: \: \: \: x + y + x - y = 4 + \frac{18}{5} \\ \\ \\ \\ \\ 2x = \frac{38}{5 } \\ \\ \\ \\ x = \frac{19}{5} \\ \\ \\ \\ \\ \\ \frac{19}{5} - \frac{18}{5} = y \\ \\ \\ \\ \\ y = \frac{1}{5}$