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4 years ago

Is the system of equations is consistent, consistent and coincident, or inconsistent? y=−x−13y=−3x+2

Mathematics

2 answers:

Klio2033 [76]4 years ago

6 0

Its inconsistent .......

UkoKoshka [18]4 years ago

4 0

Answer:

The System of Equation is Consistent.

Step-by-step explanation:

Given: System of equations y = -x - 13 and y = -3x + 2

To find: System of equation is consistent or inconsistent

System of equation is consistent if it has a unique solution or infinitely many solution and it is in consistent if it has no solution.

So we check if given system of equation has unique solution or infinitely many solution or no solution by checking their ratio.

Rewrite the system of equation,

x + y +13 = 0 and 3x + y - 2 = 0

$a_1=1\:,\:b_1=1\:,\:c_1=13\:and\:a_2=3\:,\:b_2=1\:,\:c_2=-2$

Now,

$\frac{a_1}{a_2}=\frac{1}{3}$

$\frac{b_1}{b_2}=\frac{1}{1}$

$\frac{c_1}{c_2}=\frac{13}{-2}$

Since, $\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$

Thus, System of equation has unique solution.

Therefore, The System of Equation is Consistent.

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3 years ago

A tissue can be 0.000075 meters thick.

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Answer:

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4 years ago

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3 years ago

Please answer this for me

coldgirl [10]

In 1-4, to determine whether a sequence is either arithmetic or geometric, you need to look at differences of consecutive terms (arithmetic) and ratios of consecutive terms (geometric). If you can't find it, the sequence will fall under the "neither" category.

For example, the differences between consecutive terms in the first sequence are

$\left\{2-4,\dfrac12-2,\dfrac14-\dfrac12,\ldots\right\}=\left\{-2,-\dfrac32,-\dfrac14,\ldots\right\}$

If the sequence was arithmetic, the difference between consecutive terms would have been the same constant throughout this list. But that's not the case, so this sequence is not arithmetic.

The ratios between consecutive terms are

$\left\{\dfrac24,\dfrac{\frac12}2,\dfrac{\frac14}{\frac12},\ldots\right\}=\left\{\dfrac12,\dfrac14,\dfrac12,\ldots\right\}$

The sequence would have been geometric if the list contained the same value throughout, but it doesn't. So this sequence is neither arithmetic nor geometric.

Meanwhile, in the second sequence, the differences are

$\{-1-(-6),4-(-1),9-4,\ldots\}=\{5,5,5,\ldots\}$

so this sequence is arithmetic.

In 5-6, you know the sequences are arithmetic, so you know that they follow the recursive rule

$a_n=a_{n-1}+d$

For example, in the fifth sequence we know the first term is $a_1=4$ . The common difference between terms is $d=9-4=5$ . So using the rule above, we have the pattern