Question

resolva o seguinte sistema

2a+3b=11
a+5b=16

Answer 1

{2a+3b = 11
{ a +5b= 16 .(-2)

-2a-10b= -32
2a+3b = 11
—————————
0 -7b = - 21
-7b=-21 .(-1)
7b=21
b= 21/7
b= 3

2a+3b=11
2a+3.3= 11
2a+9= 11
2a= 11-9
2a= 2
a= 2/2
a= 1

a= 1 b= 3

Answer 2

$\begin{cases} 2a+3b=11 \\ a+5b=16\end{cases}$.

Da segunda equação, $a=16-5b$. Substituindo na primeira:

$2(16-5b)+3b=11~~\Rightarrow~~32-10b+3b=11~~\Rightarrow~~10b-3b=32-11$

$7b=21~~\Rightarrow~~b=\dfrac{21}{7}~~\Rightarrow~~\boxed{b=3}$.

$a=16-5\cdot3~~\Rightarrow~~a=16-15~~\Rightarrow~~\boxed{a=1}$.