Question

$\left \{ {5x -3y=9} \atop {4x-2y=16} \right.$

Answer 1

$\boxed{\mathsf{ \left \{ {{5x-3y=9} \atop {4x-2y=16}} \right. }}\\ \\ \\ \mathsf{5x-3y=9}\\ \\ \mathsf{5x=9+3y}\\ \\ \boxed{\mathsf{x=\frac{9+3y}{5}}}\\ \\ \\ \mathsf{4x-2y=16}\\ \\ \mathsf{4(\frac{9+3y}{5})-2y=16}\\ \\ \mathsf{\frac{36}{5}+\frac{12y}{5}-2y=16}\\ \\ \mathsf{\frac{36+12y-10y}{5}=16}\\ \\ \mathsf{36+2y=80}\\ \\ \mathsf{2y=80-36}\\ \\ \mathsf{2y=44}\\ \\ \mathsf{y=\frac{44}{2}}\\ \\ \boxed{\mathsf{y=22}}$

$\mathsf{x=\frac{9+3y}{5}}\\ \\ \mathsf{x=\frac{9+3\cdot22}{5}}\\ \\ \mathsf{x=\frac{9+66}{5}}\\ \\ \mathsf{x=\frac{75}{5}}\\ \\ \boxed{\mathsf{x=15}}$

Answer 2

Olá, boa noite ☺

Resolução:

{5x - 3y = 9.  (2)
{4x - 2y = 16 (-3)
----------------------
{10x - 6y = 18.
{-12x + 6y = -48
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-2x=-30. (-1).
2x=30.
x=30/2.
x=15.

Valor de y(1ª equação):

5x - 3y = 9.
5*15 - 3y = 9.
75 - 3y =9.
-3y=9-75
-3y=-66.
3y=66.
y=66/3.
y=22.

S={15,22}

Bons estudos :)