Question

1)calcule os sistemas de equaçao
A)3×+Y=11
X+5Y=7
B)4X-Y=2
X+Y=1
C)20X+Y=44
X+5Y=25
D)10X-5Y=11
2X-4Y=18

Answer 1

a)

\left \{ {{3x+y=11} \atop {x+5y=7}} \right.\\\\x+5y=7\\x=7-5y\\\\3x+y=11\\3(7-5y)+y=11\\21-15y+y=11\\21-14y=11\\-14y=11-21\\-14y=-10^{.(-1)}\\ 14y=10\\y=\frac{10}{14} \\\\y=\frac{5}{7}\\\\

x=7-5y\\

x=7-5.\frac{5}{7} \\

x=7-\frac{25}{7} \\

x=49-25\\

x=24

S={24,$\frac{5}{7}$}

b)

$\left \{ {{4x-y=2} \atop {x+y=1}} \right. \\\\x+y=1\\x=1-y\\\\4(1-y)-y=2\\4-4y-y=2\\-5y=2-4\\-5y=-2^{.(-1)}\\ 5y=2\\y=\frac{2}{5}\\\\x=1-y\\x=1-\frac{2}{5}\\x=5-2\\x=3$

S={3,$\frac{2}{5}$}

c)

$\left \{ {{20x+y=44} \atop {x+5y=25}} \right. \\\\x+5y=25\\x=25-5y\\\\20(25-5y)+y=44\\500-100y+y=44\\500-99y=44\\-99y=44-500\\-99y=-456^{.(-1)}\\ 99y=456\\y=\frac{456}{99}\\\\ y=\frac{152}{33}\\\\x=25-5y\\x=25-\frac{152}{33} \\x=825-152\\x=673$

S={673,$\frac{152}{33}$}

d)

$\left \{ {{10x-5y=11} \atop {2x-4y=18}} \right. \\\\\left \{ {{10x-5y=11} \atop {2x-4y=18(:2)}} \right. \\\\\left \{ {{10x-5y=11} \atop {x-2y=9}} \right. \\\\x-2y=9\\x=9+2y\\\\10(9+2y)-5y=11\\90+20y-5y=11\\15y=11-90\\15y=-79\\y=\frac{-79}{15}\\\\x=9+2.\frac{-79}{15}\\\\x=9-\frac{158}{15} \\x=135-158\\x=-23$

S={-23,$\frac{-79}{15}$}