Question

http://prntscr.com/nvible

Answer 1

@Narad

Answer 2

If a system has only one solution, it is called consistent and independent

Answer 3

http://prntscr.com/nvid0e

Answer 4

The system has one solution where the red line cuts the green line.

Answer 5

so yes?

Answer 6

Yes

Answer 7

http://prntscr.com/nvie4p

Answer 8

The solution is the intersection of the red and green lines.

It is (-7,2), option B

Answer 9

okay

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Answer 10

The equations are
\[3y-2x=11\]
and
\[y=9-2x\]
Substituting the value of y in the first equation
\[3(9-2x)-2x=11\]
\[27-6x-2x=11\]
\[8x=27-11=16\]
\[x=2\]
and
\[y=9-2x=9-2*2=9-4=5\]
The solution is (2,5), this is option A

Answer 11

Got it

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Answer 12

The equations are
\[y=x+3\]
and
\[y=2x-4\]
Therefore,
\[x+3=2x-4\]
\[2x-x=3+4=7\]
\[x=7\]
and
\[y=7+3=10\]
The solution is (7,10) and this is option B

Answer 13

Okay

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Answer 14

Question nº9
The equations are
\[x+y=4\]
and
\[2x+3y=9\]
Multiplying the first equation by 2
\[2x+2y=8\]
Subtacting this equation from the second equation
\[(2x-2x)+(3y-2y)=9-8\]
\[y=1\]
and
\[x=4-y=4-1=3\]
The solution is (3,1), this is option A

Answer 15

Question nº7
The solutions are
\[2x-5y=22\]
and
\[2x-3y=6\]
Subtracting the second equation from the first
\[2x-2x-5y+3y=22-6=16\]
\[-2y=16\]
\[y=-8\]
Plugging this value in the first equation
\[2x=5y+22=5*-8+22=-40+22=-18\]
\[x=-9\]
The solution is (-9,-8)and is option B

Answer 16

Question nº8
The matrix associated with the system is
\[\left[\begin{matrix}3 & -2 \\ 3 & 2\end{matrix}\right]*\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}31 \\ -1\end{matrix}\right)\]
The augmented matrix is
\[\left[\begin{matrix}3 & -2&31 \\ 3 & 2&-1\end{matrix}\right]\]
Perform the row operations
R1<-R1+R2
R2<-R2-R1
\[\left[\begin{matrix}6 & 0&30 \\ 0 & 4&-32\end{matrix}\right]\]
Perform the row operations
R1<-R1/6
R2<-R2/4
\[\left[\begin{matrix}1 & 0&5 \\ 0 & 1&-8\end{matrix}\right]\]
The solution is (5,-8) and this is option (A)

Answer 17

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Answer 18

Question nº9
Rewrite the equations as
\[2x-y=1\] and
\[6x-y=13\]
The augmented matrix is
\[\left[\begin{matrix}2 & -1&1 \\ 6 & -1&13\end{matrix}\right]\]
Perform row operations
R2<R2- 3R1
\[\left[\begin{matrix}2 & -1&1\\ 0 & 2&10\end{matrix}\right]\]
R2<- R2/2
\[\left[\begin{matrix}2 & -1&1\\ 0 & 1&5\end{matrix}\right]\]
R1<-R1+R2
\[\left[\begin{matrix}2 & 0&6 \\ 0 & 1&5\end{matrix}\right]\]
R1<- R1/2
\[\left[\begin{matrix}1 & 0&3 \\ 0 & 1&5\end{matrix}\right]\]
The solution is (3,5 and is option A

Answer 19

Question nº10
Let volume of 10% saline sol be =x

Volume of 4% saline solution is =500-x

The mass balance equation is
\[x*10/100+(500-x)*4/100=500*6/100\]
\[0.1x+20-0.04x=30\]
\[0.06x=30-20=10\]
\[x=10/0.06=167mL\]
and
\[500-167=333mL\]
The answer is option B

Answer 20

okay

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Answer 21

The graph is attached

Answer 22

but how would I draw that on the graph I ss?

Answer 23

Identify 2 points on eah line and draw them
First line, (0, -2) and (-1, 4), discontinued line

Second line, (0, -10) and (2,0), discontinued line

The third line is the x-axis, continued line

The zone is the light green part

Answer 24

http://prntscr.com/nvk7oz

Answer 25

is this good?

Answer 26

Yes, the red line and the blue line are discontinued
And color the zone south of the intersection of the red and blue line

Answer 27

Discontinued line = dotted line