Question

http://prntscr.com/nuzpfo

Answer 1

@Narad

Answer 2

The second equation is
\[8x+y+4=0\]
This is the same as the first equation.
The system is consistent since
\[y=-8x-4\]
For any value of x, we can find a value ofy

Answer 3

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Answer 4

The second equation is
\[-14x-4y+2=0\]
\[-7x-2y+1=0\]
\[7x+6=-2y\]
Therefore,
\[7x+1=7x+6\]
\[1=6\]
The system is inconsistent

Answer 5

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Answer 6

The second equation is the same as the first one by multiplying by 5.

Therefore, there is only one equation with an infinity of solutions (x,y)

The system is consistent.

Answer 7

Okay

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Answer 8

The equations are

\[2y=x-7\]
and
\[6y=-2x+14\]
The equations has one solution (7,0)

The system is consistent

Answer 9

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Answer 10

The equations are
\[y=2x+5\] and
\[y=2x-2\]
The system has no solutions and are therefore, inconsistent

Answer 11

Got it

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Answer 12

The equations are
\[3y=8+2x\] and
\[y=3x+5\]
Multiplying the second equation by 3
\[3y=9x+15\]
Therefore,
\[8+2x=9x+15\]
Solving for x
\[7x=-7\]
\[x=-1\]and
\[y=3x+5=3*-1+5=2\]
The solutions are (-1,2)

Answer 13

Okay

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Answer 14

The equations are
\[y=4x-8\] and
\[2y=8x-5\]
Multiplying the first equation by 2
\[2y=8x-16\]
Therefore
\[8x-5=8x-16\]
\[-5=-16\]
There are no solutions and the system is inconsistent.

Answer 15

okay

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Answer 16

The equations are
\[y=-5x+13\] and
\[3y=15-3x\]
Dividing the last equation by 3
\[y=5-3x\]
Therefore,
\[-5x+13=5-3x\]
Solving for x
\[2x=13-5=8\]
\[x=2\] and
\[y=-5*2+13=3\]
The system is consistent and has one solution (2,3)

Answer 17

Got it

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Answer 18

The equations are
\[2x=36-4y\]
\[x=18-2y\] and
\[10y=5\]
\[y=2\] and
\[x=18-2*2=18-4=14\]
The system is consistent and has one solution (14,2)

Answer 19

okay

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Answer 20

The equations are
\[2x=4y+12\]
That is
\[x=2y+6\] and
\[3x=6y+21\]
That is
\[x=2y+7\]
Therefore,
\[2y+6=2y+7\]
\[6=7\]
The system has no solutions and is inconsistent.

Answer 21

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Answer 22

The equations are
\[2x=9y+32\] and
\[4x=-y-12\]
Therefore, by multiplying the first equation by 2
\[4x=18y+64\]
So,\[18y+64=-y-12\]
\[19y=-64-12=-76\]
\[y=-76/19=-4\]
\[x=(9*-4+32)/2=-4/2=-2\]
The system is consistent and has one solution (-4,-2)

Answer 23

okay

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Answer 24

The 2 equations are the same
\[y=3x+1\]
This system has an infinity of solutions and is consistent

Answer 25

okay

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Answer 26

The equations are
\[x=2y+4\] and
\[2x=3y+8\]
Multiplying the first equation by 2
\[2x=4y+8\]
Therefore,
\[3y+8=4y+8\]
\[y=0\] and
\[x=4\]
The system has one solution (4,0) and is consistent

Answer 27

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Answer 28

The equations are
\[2x=5y-3\] and
\[x=2y-3\]
Therefore,
\[2x=4y-6\] and
\[5y-3=4y-6\]
\[y=-3\] and
\[x=2*-3-3=-6-3=-9\]
The system has one solution (-9, -3) and is consistent

Answer 29

okay

last one
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Answer 30

The equations are
\[3x=8-4y\] and
\[2x=5y-3\]
Multiplying the first equation by 2 and the second equation by 3 and comparing
\[6x=16-8y\] and
\[6x=15y-9\]
Therefore,
\[16-8y=15y-9\]
\[23y=25\]
\[y=23/25\]
and
\[x=(5*23/25-3)/2=(23/5-3)/2=8/10=4/5\]
The solutions are (4/5, 23/25) and is consistent

Answer 31

Okay thank you

Answer 32

There is a correction to the last one
\[y=25/23\]
and
\[x=28/23\]