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kolbaska11 [484]
2 years ago
14

Determine which system below will produce infinitely many solutions.

Mathematics
1 answer:
DaniilM [7]2 years ago
4 0
<span>A.  −6x + 3y = 18 4x − 3y = 6
B   2x + 4y = 24 6x + 12y = 36
C.  3x − y = 14 −9x + 3y = −42
D.  5x + 2y = 13 −x + 4y = −6

For infinitely many solutions,  we are looking for linearly dependent equations, which means that one equation is an exact multiple or sub-multiple of the other.
Example: 
</span>2x + 4y = 24
6x + 12y = 36
<span>is a system that does NOT have a solution, because 6/2=3 for x, 12/4=3 for y, but 36/24=1.5.  The two lines have the same slope (therefore parallel), but they have different y-intercepts.  So the two lines will never meet, and therefore no solution.


or another example:
</span>  3x  -y = 14
  -9x + 3y = -42
We see that -9/3=-3, 3/-1=-3, -42/3=-14, this system has coefficients all in the same ratio, meaning that the lines are coincident (and linearly dependent), therefore infinitely many solutions.

Still another example:
−6x + 3y = 18
4x − 3y = 6
we see that 18/6=3, 3/(-3)=-1 , since the ratios are different, the two equations are not linearly dependent, and therefore the system has unique solution.

Last example:
5x + 2y = 13
−x + 4y = −6
Check the ratio of the coefficients:
-1/5=-1/5
4/2=2  ..... we can stop here and conclude that there is a unique solution because the equations are not in the same ratio. (unique means that there is exactly one solution)

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19. If the pg", and "terms of an A.P. are a,b, and c respectively. prove that: p(b-c) + (ca) + rſa-b) = 0 50 Approved by Curricu
professor190 [17]

Answer:

Step-by-step explanation:a = m + (p-1)*d

b = m + (q-1)*d

c = m + (r-1)*d

p(b-c) = p*(q-r)*d

q(c-a) = q*(r-p)*d

r(a-b) = r*(p-q)*d

p(b-c)+q(c-a)+r(a-b)

= p*(q-r)*d + q*(r-p)*d +r*(p-q)*d

= (pq-pr+qr-pq+rp-qr)*d

= 0*d = 0

So i prove p(b-c)+q(c-a)+r(a-b)=0 hope this is helpfull

4 0
3 years ago
What is the first operation used to evaluate 13-2x3+4 divided by 4+4
lisabon 2012 [21]

Answer:

  multiplication

Step-by-step explanation:

The evaluation of ...

  13 -2·3 +4/4 +4

starts with the multiplication, because there are no exponents or parentheses.

  13 -6 +4/4 +4

Next is the division:

  13 -6 +1 +4

Finally, the addition and subtraction:

  7 +1 +4

  8 +4

 12

_____

We have assumed your x is not a variable, but is intended to indicate multiplication. We have also assumed that your "divided by" implies no particular grouping, so that the numerator is the first preceding number and only the first following number is in the denominator.

6 0
3 years ago
Need more help please!!
IrinaK [193]
46: 24a+40

First we are going to take a look at a) 8(3a+5)

a) We then simplify it by multiplying the numbers inside the parenthesis by 8.

a) 24a+40

Now we ask ourselves, is this equivalent to 24a+40? YES! 

So your answer for #46 is a)   8(3a+5)


7 0
3 years ago
What is the cube root of negative 8?
Nana76 [90]
Cbrt-8 = -2
..........
5 0
3 years ago
Consider right triangle MNO below which expression represents the length of side MN
azamat

Answer:

I can help you via Watsapp

5 0
2 years ago
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