Question

Resolver o sistema

3x/4+2y/5=4x/3-19y/40

x/3+y/4= 1/4

Answer 1

╠> 3x/4+2y/5=4x/3-19y/40 → mmc(3,4,5,40) = 2³ x 3 x 5 = 120
╠> x/3+y/4= 1/4 → mmc(3,4) = 12

╠> 30*3x/120 + 24*2y/120 = 40*4x /120 - 3*19y/120
╠> 4x/12 + 3y/12= 3/12 

╠> 90x/120 + 48y/120 = 160x /120 - 57y/120
╠> 4x/12 + 3y/12= 3/12 

╠> 90x + 48y = 160x - 57y
╠> 4x + 3y = 3

╠> 90x -160x + 48y + 57y = 0 
╠> 4x + 3y = 3

╠> -70x + 105y = 0 → (÷35)
╠> 4x + 3y = 3
 
╠> -2x + 3y = 0 
╠> 4x + 3y = 3

╠> -2x = - 3y ↔ -2x = - 3y (-1) ↔ 2x = 3y ↔ x = (3/2)*y
╠> 4x + 3y = 3

4 [(3/2)*y] + 3y = 3 ↔ 6y + 3y = 3 ↔ 9y = 3 ↔ y = 3/9 ↔ y = 1/3
▲ y = 1/3
▲ x = (3/2) * (1/3) = 3/6 = 1/2
▲ x = 1/2

S={(1/2;1/3)}

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Obrigado pela oportunidade 
Boa sorte, bons estudos!
SSRC - 2015 
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