Решите систему уравнений:
1)
5x + y = 30
3x - 4y = 41
2)
3u - 4v = 2
9u - 5v = 7
3)
5y + 8z = 81
10y - 3z = -15
Ответы
Ответ дал:
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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. 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.](https://tex.z-dn.net/?f=+left+%7B+%7B%7B5x%2By%3D30%7D+atop+%7B3x-4y%3D41%7D%7D+right.++%5C+%5C+++left+%7B+%0A%7B%7B20x%2B4y%3D120%7D+atop+%7B3x-4y%3D41%7D%7D+right.%2B++%5C++%5C+20x%2B3x%3D120%2B41+%5C+%0A23x%3D161+%5C+x%3D7+%5C++%5C+5x%2B7%3D30+%5C+5%2A7%2By%3D30+%5C+35%2By%3D30+%5C+y%3D-5+%5C++%5C+%0Aotvet%3A%287%3B-5%29+%5C++%5C+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} ) 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} )](https://tex.z-dn.net/?f=+left+%7B+%7B%7B3u-4v%3D2%7D+atop+%7B9u-5v%3D7%7D%7D+right.++%5C++left+%7B+%0A%7B%7B9u-12v%3D6%7D+atop+%7B9u-5v%3D7%7D%7D+right.+-+%5C++-12v%2B5v%3D6-7+%5C+-7v%3D-1+%5C+v%3D+%0Afrac%7B1%7D%7B7%7D++%5C++%5C+3u-4%2A+frac%7B1%7D%7B7%7D+%3D2+%5C+3u-+frac%7B4%7D%7B7%7D+%3D2+%5C+3u%3D2+%0Afrac%7B4%7D%7B7%7D%3D+frac%7B18%7D%7B7%7D+%5C++%5C+u%3D+frac%7B6%7D%7B7%7D++%5C++%5C+otvet+%3A%28++%0Afrac%7B6%7D%7B7%7D+%3B+frac%7B1%7D%7B7%7D+%29)
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} ) 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} )](https://tex.z-dn.net/?f=+left+%7B+%7B%7B5y%2B8z%3D81%7D+atop+%7B10y-3z%3D-15%7D%7D+right.++%5C++left+%7B+%7B%7B10y%2B16z%3D162%7D+atop+%7B10y-3z%3D-15%7D%7D+right.+-+%5C+16z%2B3z%3D162%2B15+%5C+19z%3D177+%5C+z%3D+frac%7B177%7D%7B19%7D+%3D9+frac%7B6%7D%7B19%7D++%5C++%5C+10y-3%2A+frac%7B177%7D%7B19%7D%3D-15+%5C++%5C+10y-+frac%7B531%7D%7B19%7D++%3D-15+%5C++%5C+10y%3D-15%2B+frac%7B531%7D%7B19%7D+%3D-15%2B27+frac%7B18%7D%7B19%7D+%3D12+frac%7B18%7D%7B19%7D+%3D+frac%7B246%7D%7B19%7D++%5C++%5C+y%3D+frac%7B246%7D%7B190%7D+%3D1+frac%7B56%7D%7B190%7D++%5C++%5C+otvet%3A%281+frac%7B56%7D%7B190%7D+%3B9+frac%7B6%7D%7B19%7D+%29)
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