Question

Help Fast please with system of equations! Please!




Classify the system and determine the number of solutions. (Check all that apply. )
3x - y + 2z = 4
2x - y + 3z = 7
-9x + 3y - 6z = -12

infinitely many solutions
inconsistent
consistent
no solution

Answer 1

hint : first equation and last equation are same

Answer 2

How are they?

Answer 3

take first equation,
multiply -3 both sides, wat do u get ?

Answer 4

the last one :p

Answer 5

so does that mean that they cancel out?

Answer 6

nope, when both equations are same,
that means they're overlapping.... so there are infinite solutions

Answer 7

:O

Answer 8

Thank you :D

Answer 9

np :)

Answer 10

Can you help me with one more?

Answer 11

sure :)

Answer 12

Classify the system and determine the number of solutions. (Check all that apply.)
x - 2y = -8
4x = 8y - 56

no solution
infinitely many solutions
consistent
inconsisten

Answer 13

multiply the first equation wid 4
wat do u get ?

Answer 14

4x-8y=-32

Answer 15

yes :) put the second equaiton also in standard form

Answer 16

second equation :-

4x = 8y - 56

4x - 8y = - 56

Answer 17

so these two equations are DIFFERENT.
but clearly they have same slopes. so ?

Answer 18

Basically they are parallel?

Answer 19

yup,
they're parallel cuz they have same slope.

they're NOT overlapping either

Answer 20

those two line are like, the train tracks.... they go forever, they never meet

Answer 21

so NO solution

Answer 22

So that would be inconsistent no solution

Answer 23

Correct !
when u dont have solutions, we call it a inconsistent system

Answer 24

Thank you, You have been a life saver :D

Answer 25

np =))

Answer 26

Question Could you check this last thing for me before I submit it

Answer 27

sure :) you may ask any number of questions... this need not be the last thing lol ;)

Answer 28

Lol :p Thank you

Answer 29

I chose the third answer o.o

Answer 30

because it has to be at least or equal to 90 right?

Answer 31

Yes ! you're right ! good job !!

Answer 32

XD THank you one more sorry I just really want to do good on this test

Answer 33

I chose the second one o.o

Answer 34

because does it not mean when it is > or < doesn't that mean it is a dashed line instead of solid

Answer 35

sorry was afk,,
one sec let me check :)

Answer 36

lol Nevermind man :p 30 seconds before i have to submit

Answer 37

I was right :p I scored a 98% :D

Answer 38

wow ! congrats !!
but still u missed one or two it seems.... its not 100%

Answer 39

I missed one :p I mixed up a definition ._.

Answer 40

ahh still its good :) aim for 100 next time !

Answer 41

I shall :p Thank you so so so so so so much

Answer 42

np :D

Answer 43

You really helped me out :3 I despise system of equations so much

Answer 44

@ganeshie8 can we use this as help for this

Answer 45

yep
wats the question again :)

Answer 46

By the way the teacher gave my last point i missed back so... i got 100% :p

Answer 47

oh cool 98+1 = 100 is it :P

Answer 48

xD it was worth 2 points so :p the calculation does work xD

Answer 49

given two equations,
u knw how to write the matrix form ? Ax = b ?

Answer 50

Well I have some knowledge on how to do this

Answer 51

basically you have to move the variables on one side

Answer 52

so \[5x + 9y = 1\]
and
\[4x - 7y = \]

Answer 53

=2

Answer 54

nevermind that is for finding the determinant .-. *sigh*

Answer 55

if the two equation are below :-
\(a_1x + b_1y = c_1\)
\(a_2x + b_2y = c_2\)

then, matrix equation wud be :-
\[

\left[ \begin{array}{cc}
a_1 & b_1 \\
a_2 & b_2 \\

\end{array} \right]
\left[ \begin{array}{cc}
x \\
y \\

\end{array} \right]
=

\left[ \begin{array}{cc}
c_1 \\
c_2 \\

\end{array} \right]

\]

Answer 56

ok

Answer 57

so then what is the x and y ?

Answer 58

if the two equation are below :-
\(5x+9y = 1\)
\(-4x-7y = 2\)

then, matrix equation wud be :-

????

Answer 59

you got the matrix equation part of the question ?

Answer 60

just from knowing the form of matrix equation, u can strike off two options : A and C

Answer 61

so answer is between B and D

Answer 62

would it be B?

Answer 63

Or is the 1 and the 2 stand or the x and y values?

Answer 64

obviously B is correct,
but how did u get ?

Answer 65

Because D has the equals as the x and y values and that is false

Answer 66

you simply tested whether the given x, y values are satisfying given equations or not is it ? Nice :)
lets do next problem

Answer 67

for the next one would it be B? Because its the right format and it doesn't use the equals as the x and y variables

Answer 68

B is correct !
i dint get wat do u mean by : "it doesnt use the equals as x and y variables" :|

Answer 69

Well you see how the answer is 3 and 1

Answer 70

c1 and c2 they are the answers to the equations that you got them from so... it obvious that it isn't the answer

Answer 71

okie got u :)

Answer 72

the next problem is different from the other onces

Answer 73

you knw how to find the \(determinant\) ?

Answer 74

yes

Answer 75

its like cross multiplying and then subtracting

Answer 76

If the matrix is
\[

\left[ \begin{array}{cc}
a_1 & b_1 \\
a_2 & b_2 \\

\end{array} \right]

\]
then, its inverse is :-

\[ \frac{1}{determinant}

\left[ \begin{array}{cc}
b_2 & -b_1 \\
-a_2 & a_1 \\

\end{array} \right]

\]

Answer 77

memorize that for the rest of ur time in matrices chapter

Answer 78

lol This is the last part of the chapter actually :p

Answer 79

yes, first find \(determinant\) for given matrix
wat do u get ?

Answer 80

good you're lucky :)

Answer 81

let me see .165 -.16 ??

Answer 82

\(determinant = \frac{1}{2}\times \frac{1}{3} - 0 \times \frac{-1}{6}\)

Answer 83

thats 0

Answer 84

I put them into fractions lol

Answer 85

decimals *

Answer 86

\(determinant = \frac{1}{2}\times \frac{1}{3} - 0 \times \frac{-1}{6}\)

\(=\frac{1}{6} - 0\)

\(=\frac{1}{6} \)

Answer 87

you need to learn to be bit lazy lol
dont do anything unless it is inevitable

Answer 88

xD So. Keep them as fractions?

Answer 89

yup ! Always

Answer 90

so can you do the multiplying for me i can't do fractions lol

Answer 91

\[Inverse ~~~ = ~~~
\frac{1}{determinant}

\left[ \begin{array}{cc}
b_2 & -b_1 \\
-a_2 & a_1 \\

\end{array} \right]
\]

\[~~~~~~~~~~~~~~~ ~~~ = ~~~
\frac{1}{\frac{1}{6}}

\left[ \begin{array}{cc}
\frac{1}{3} & 0 \\
\frac{1}{6} & \frac{1}{2} \\

\end{array} \right]
\]


\[~~~~~~~~~~~~~~~ ~~~ = ~~~
6

\left[ \begin{array}{cc}
\frac{1}{3} & 0 \\
\frac{1}{6} & \frac{1}{2} \\

\end{array} \right]
\]

\[~~~~~~~~~~~~~~~ ~~~ = ~~~


\left[ \begin{array}{cc}
2 & 0 \\
1 & 3 \\

\end{array} \right]
\]

Answer 92

see if that makes some sense

Answer 93

So 6 is the determinant. You multiplied 6 by each of the numbers and got 2 0 1 3