Find The Next Number 12 13 15 17 111 113 117 119 123 ?

Mathematics

1 answer:

Temka [501]3 years ago

5 0

The Next Number is 129.

These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1.

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Solve the linear system of equations using the linear combination method. {8a−4b=205a−8b=62

11Alexandr11 [23.1K]

Sorry I am a little late...

a = -2

b = -9

Here is how to solve the problem.

First thing I did was multiply the first equation by -2 so that we can eliminate the the b. After you multiply it by -2, your new equation is -16a + 8b = -40.

You leave the second equation alone and all you do is combine like terms. So -16a+5a is -11. And you eliminate the b. Then you're going to do -40+62 which is 22. So it's -11a=22 and then you have to solve for a. What I did was I multiplied the whole thing by minus to turn the a positive. So then it's 11a=-22. Pretty easy, the final step is to simplify. -22/11 is -2. ;D

So there you have your first answer.

a = -2

Now we're going to use the first answer to help us find b.

For the second equation, all you're going to do is plug in that a.

5 (-2)-8b=62

-10 - 8b = 62

Now we move the -10 to the other side...

-8b = 62 + 10

-8b = 72

Multiply the whole thing by negative once again to turn the b positive.

Now we have 8b = -72

The final step is to simplify. -72/11 = -9

b = -9

Hope this makes sense! Also I had the same question on my test and I got it right. :)