Question

RESOLVA

{2x- y²=1
{3x+Y=4

Answer 1

2x - y2 = 1
3x + y = 4 ( y = 4 - 3x )

2x - y2 = 1
2x - ( 4 - 3x ) 2 = 1
2x - ( 16 - 24x + 9x2 ) = 1
2x - 16 + 24x - 9x2 = 1
-9x2+ 2x + 24x - 16 - 1 = 0
- 9x2 + 26 x - 17 = 0 ( inverter os sinais )
9x2 - 26x + 17 = 0
∆ = 676 - 612
∆ = 64

X1 = ( 26 + 8 ) / 18
X1 = 34 / 18( simplificar )
X1 = 17 / 9
X2 = ( 26 - 8 ) / 18
X2 = 18 / 18
X2 = 1

y = 4 - 3x
y = 4 - 3• 17 / 9
y = 4 - 17 / 3
y= 12 /3 - 17 / 3
y = - 5 / 3

y = 4 - 3x
y = 4 - 3
y = 1

os valores de x são : 17 / 9 e 1
os valores de y são : - 5 / 3 e 1

Answer 2

Vamos lá

{2x - y² = 1   (I)

{3x + y = 4 (II)

de (II) vem

y = 4 - 3x, y² = 16 - 24x + 9x²

de (I) vem

2x - 16 + 24x - 9x² = 1

9x² - 26x + 17 = 0

delta

d² = 26² - 4*9*17 = 64 , d = 8

x1 = (26 + 8)/18 = 34/18 = 17/9

x2 = (26 - 8)/18 = 18/18 = 1

agora

3x1 + y1 = 4

51/9 + y1 = 36/9, y1 = -15/9 = -5/3

3x2 + y2 = 4

3 + y2 = 4, y2 = 1

S = (17/9, -5/3),(1, 1)