Question

Determinati nr reale x,y pt care (2-3i)·x + (4+i)·y = 10-i

Answer 1

   
[tex](2-3i)\cdot x +(4+i)\cdot y = 10 - i \\ 2x - 3xi + 4y+yi = 10 - i \\ \\ \text{rezolvam sistemul de ecuatii:} \\ \\ 2x + 4y = 10 \\ -3x + y = -1 ~~~\Longrightarrow ~~ \boxed{y=-1+3x~~~~~(Substitutie)}\\ --- \\ \\ 2x+4(-1+3x) = 10 \\ 2x - 4+12x=10 \\ 14x = 10+4 \\ 14x = 14 \\ \\ \displaystyle x = \frac{14}{14} =\boxed{1 }\\ \\ y = 1 + 3x = -1 + 3\cdot 1 = -1 + 3= \boxed{2} [/tex]