Question

3(x-2)-2(y+1)=-1 5(x+3)-8(y-2)=45 ​

Answer 1

Я не поняла что именно нужно делать,ну вроде так...

1.Я записываю как систему уравнений

{3(x-2)-2(y+1)=45

{-15(x+3)-8(y-2)=45 -2 Скобки идут как 1 большая

2. Упрощаю выражение

{3x-2y=53

{-15(x+3)-8(y-2)=45 -2 Скобки идут как 1 большая

3.{3x-2y=53

{-15x-8y=74

Умножаем обе части на 5

15x-10y=265

-15x-8y=74

-18y=339

y=-113/6

3x-2*(-113/6)=53

x=46/9

Ответ:X=46/9; y=-113/6

Answer 2

We are given the system of two linear equations:

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3(x-2)-2(y+1)=-1    ... (1)
5(x+3)-8(y-2)=45    ... (2)

We can solve this system using any of the standard methods such as substitution or elimination. Here, we will use the elimination method:

Step 1: Multiply equation (1) by 5 and equation (2) by 3 to eliminate the x terms:

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15(x-2)-10(y+1)=-5   ... (1')   [5 times equation (1)]
15(x+3)-24(y-2)=135  ... (2')   [3 times equation (2)]

Step 2: Simplify the above equations:

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15x - 30 - 10y - 10 = -5      ... (1')
15x + 45 - 24y + 48 = 135    ... (2')

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15x - 10y - 35 = 0           ... (1'')
15x - 24y + 93 = 0           ... (2'')

Step 3: Multiply equation (1'') by 12 and add it to equation (2'') to eliminate the x terms:

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180x - 120y - 420 = 0        ... (1''')  [12 times equation (1'')]
15x - 24y + 93 = 0           ... (2'')

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180x - 120y - 420 = 0
  0x - 192y - 327 = 0

Step 4: Solve for y:

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-192y - 327 = 0
-192y = 327
y = -327/192

Step 5: Substitute y = -327/192 into either equation (1) or (2) to solve for x:

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3(x-2)-2(-327/192+1)=-1
3(x-2)+654/192=-1
3(x-2)=-1-654/192
3(x-2)=-846/192
x-2=-282/192
x=-282/192+2
x=-22/16
x=-11/8

Step 6: Check the solution:

Substitute x = -11/8 and y = -327/192 into both equations:

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3(x-2)-2(y+1)=-1
3(-11/8-2)-2(-327/192+1)=-1
-33/8-48/8+327/192-2=-1
-33/8-96/8+327/192-384/192=-192/192
-129/16+327/192-384/192=-1
-207/32+327/192-96/192=-192/192
-207/32+231/192=-1
-207/32+39/32=-32/32
-168/32=-32/32
-5=-1 (FALSE)

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5(x+3)-8(y-2)=45
5(-11/8+3)-8(-327/192-2)=45
-55/8+15-656/192+16=45
-440/32+480/32-656/192+384/192=1440/32
-616/192+384/192=45
-232/192=45 (FALSE)

The solution (x,