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2 years ago

I'm trying to find out if the system have a unique solution, no solution or infinitely many solutions

Mathematics

2 answers:

Zielflug [23.3K]2 years ago

7 0

Both have no solution

kow [346]2 years ago

6 0

Alright so this is what you do.
You need to isolate one variable so that it is y = or x =
Lets go with y = for the first one

-x +3y = -6
x - 3y = 6

Isolate y = by adding x for the first one and then subtracting x from the second one.
3y = -6 + x
-3y = 6 - x

You would then divide the second one by -3 and divide by 3 in the first one.

y = (-6 +x) / 3
y = (6 -x) / -3
Since this is what y = you can put them together.

-6+x) / 3 = 6-x)/-3 (I put one parenthesis for convenience)

This equation is now set and you aren't done yet.
You can take out -1 from each side. This makes it no solution since you must always multiply by -1.
(6+x) / 3 = -1( (6+x) / 3)

Try the second one on your own!

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4. Division

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6. Subtraction

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What is the value of y in the sequence below? 2,y,18, -54,162,

snow_lady [41]

First, let's check if the sequence is geometric or arithmetric.

If arithmetric, the sequence will have common difference.

Arithmetric

$\displaystyle \large{a_{n + 1} - a_n = d}$

d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.

Geometric

$\displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}$

r stands for a common ratio.

To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.

Let's check by dividing sequences.

We have:

2,y,18,-54,162,...

Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.

$\displaystyle \large{ \frac{ - 54}{18} = - 3 } \\ \displaystyle \large{ \frac{ 162}{ - 54} = - 3}$

Hence, the sequence is geometric.

Because the common ratio is -3. Let these be the following:

$\displaystyle \large{ a_{n + 1} = y } \\ \displaystyle \large{ a_n = 2 } \\ \displaystyle \large{ r = - 3 }$

From the:

$\displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}$

Substitute the values in.

$\displaystyle \large{ \frac{y}{2} = - 3}$

Multiply the whole equation by 2 to isolate y.

$\displaystyle \large{ \frac{y}{2} \times 2 = - 3 \times 2} \\ \displaystyle \large{ y = - 6}$

Therefore, the value of y is -6.

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2 years ago