Question

3a-2b=6
a+b=42
a=?
b=?

Answer 1

a+b=42 =>a=42-b
3a-2b=6 => 3(42-b)-2b=6 (am inlocuit a-ul aflat mai sus)
126-3b-2b=6 => 126-5b=6 =>-5b=6-126 => -5b=-120 => b=24
a=42-b => a=42-24=18
a=18
b=24

Answer 2

$\displaystyle \left \{ {{3a-2b=6} \atop {a+b=42| \cdot 2}} \right. \Rightarrow \left \{ {{3a-2b=6} \atop {2a+2b=84}} \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~------- \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~5a~~~/~~=90 \Rightarrow a= \frac{90}{5} \Rightarrow \boxed{a=18} \\ \\ 3a-2b=6 \Rightarrow 3 \cdot 18-2b=6 \Rightarrow 54 -2b=6 \Rightarrow -2b=6-54 \Rightarrow \\ \\ \Rightarrow -2b=-48 \Rightarrow b= \frac{48}{2} \Rightarrow \boxed{b=24}$