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blsea [12.9K]
3 years ago
8

What is the solution to the system of equations below? -4x+6y=-18 and y=-2x+21 plz explain!

Mathematics
2 answers:
yKpoI14uk [10]3 years ago
4 0
Simple...

work is attached. :D


Mazyrski [523]3 years ago
4 0
We are given the value of y.....y = -2x + 21...so we are going to sub in -2x + 21 in for y in the other equation.

-4x + 6y = -18
-4x + 6(-2x + 21) = -18....now we distribute through the parenthesis.
-4x - 12x + 126 = -18... simplify
-16x + 126 = -18.....subtract 126 from both sides
-16x + 126 - 126 = -18 - 126....simplify
-16x = -144...now divide both sides by -16
(-16/-16)x = -144/-16...simplify
x = 9

now we can use either equation...sub in 9 for x and solve for y
y = -2x + 21
y = -2(9) + 21
y = -18 + 21
y = 3

now we can check our answers...
-4x + 6y = -18
-4(9) + 6(3) = -18
-36 + 18 = -18
-18 = -18 (correct)

so ur solution is : (9,3)
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2. Find the common difference and the recursive formula. a. 22, 19, 16, 13, …
Musya8 [376]

Answer:

The common difference d is d = -3

The recursive formula is: \mathbf{a_n=a_{n-1}-3}

Step-by-step explanation:

We need to find the common difference and the recursive formula.

a. 22, 19, 16, 13, …

First we will find common difference

The formula of arithmetic sequence is: a_n=a_1+(n-1)d

where a_n is nth term, a_1 is 1st term and d is the difference

Looking at the sequence we get: a_1=22, a_2=19

Using these values we can find d, the common difference

a_n=a_1+(n-1)d\\put\:n=2, a_2=19, a_1=22\\19=22+(2-1)d\\19=22+d\\d=19-22\\d=-3

So, the common difference d is d = -3

Now, we will find the recursive formula:

The recursive formula is of type: a_n=a_{n-1}+d

We have found common difference d = -3

So, the recursive formula will be:

a_n=a_{n-1}+d\\a_n=a_{n-1}+(-3)\\a_n=a_{n-1}-3

The recursive formula is: \mathbf{a_n=a_{n-1}-3}

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