Question

помогите решить систему уравнений ...
1) {х-3у=8
{ 2х-у=6

2) {4x-5 y=83
{2x+5y=29

Answer 1

1) x-3y=8
2x-y=6

 

2x-y=6

y=2x-6

 

x-3y=8

x-3*(2x-6)=8

-5x+10=0

x=10/5

x=2

 

2x-y=6

2*2-y=6

y=-2

2) 4x-5y=83
2x+5y=29

 

2x+5y=29

y=-0.4x+5.8

 

4x-5y=83

4x-5*(-0.4x+5.8)=83

6x-112=0

x=112/6

x=56/3

 

2*(56/3)+5y=29

25/3+5y=0

y=(-25/3)/5

y=-5/3

Answer 2

Система 1.

$ttdisplaystyle left { {{x-3y=8} atop {2x-y=6}} right. Longrightarrow left { {{x-3y=8} atop {y=2x-6}} right. \\x-3*(2x-6)=8\x-6x+18=8\-5x=8-18\-5x=-10\x=2\\y=2*2-6\y=4-6\y=-2$

Ответ: (2; -2)

Система 2.

$ttdisplaystyle +left { {{4x-5y=83} atop {2x+5y=29}} right. \----------\6x=112\\x=18frac{2}{3}\==========\\2*18frac{2}{3}+5y=29\\\2*frac{56}{3}+5y=29\\\frac{112}{3}+5y=29\\\5y=29-frac{112}{3}\\\5y=frac{87}{3} -frac{112}{3}\\\5y=-frac{25}{3}\\\y=-frac{25}{3}*frac{1}{5}\\\y=-frac{5}{3}\\\y=-1frac{2}{3}$

Ответ: $ttdisplaystyle bold{(18frac{2}{3} ; -1frac{2}{3})}$