Question

rezolvati sistemul
5x+3(y-1)=7
7(x+1)+2y=10

Answer 1

$5x + 3(y - 1) = 7\brace7(x + 1) + 2y = 10 \\ \\ 5x + 3(y - 1) = 7 \\ 5x + 3y - 3 = 7 \\ 5x = 7 + 3 - 3y \\ 5x = 10 - 3y \\ \\ x = \frac{10 - 3y}{5} \\ \\ x = 2 - \frac{3}{5} y \\ \\ \\ \implies7(x + 1) + 2y = 10 \\ \\ = 7(2 - \frac{3}{5} y + 1) + 2y = 10 \\ \\ 21 - \frac{21}{5} y + 2y = 10 \\ \\ 21 - \frac{11}{5} y = 10 \\ \\ 105 - 11y = 50 \\ - 11y = - 55 \\ \: \boxed{ y = 5} \\ \\ \iff \: x = 2 - \frac{3}{\not5} \times \not5 \\ \iff \: x = 2 - 3 \\ \implies \: \boxed{x = - 1}$