Question

Решите систему уравнений:
1)
5x + y = 30
3x - 4y = 41

2)
3u - 4v = 2
9u - 5v = 7

3)
5y + 8z = 81
10y - 3z = -15

Answer 1

1.
$left { {{5x+y=30} atop {3x-4y=41}} right. \ \ left { {{20x+4y=120} atop {3x-4y=41}} right.+ \ \ 20x+3x=120+41 \ 23x=161 \ x=7 \ \ 5x+7=30 \ 5*7+y=30 \ 35+y=30 \ y=-5 \ \ otvet:(7;-5) \ \ 2.$
2.
$left { {{3u-4v=2} atop {9u-5v=7}} right. \ left { {{9u-12v=6} atop {9u-5v=7}} right. - \ -12v+5v=6-7 \ -7v=-1 \ v= frac{1}{7} \ \ 3u-4* frac{1}{7} =2 \ 3u- frac{4}{7} =2 \ 3u=2 frac{4}{7}= frac{18}{7} \ \ u= frac{6}{7} \ \ otvet :( frac{6}{7} ; frac{1}{7} )$
3.
$left { {{5y+8z=81} atop {10y-3z=-15}} right. \ left { {{10y+16z=162} atop {10y-3z=-15}} right. - \ 16z+3z=162+15 \ 19z=177 \ z= frac{177}{19} =9 frac{6}{19} \ \ 10y-3* frac{177}{19}=-15 \ \ 10y- frac{531}{19} =-15 \ \ 10y=-15+ frac{531}{19} =-15+27 frac{18}{19} =12 frac{18}{19} = frac{246}{19} \ \ y= frac{246}{190} =1 frac{56}{190} \ \ otvet:(1 frac{56}{190} ;9 frac{6}{19} )$