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3 years ago

Solve for the following system of equations. -7x+6y=9 -2x-5y+16 x=? y=?

Mathematics

2 answers:

CaHeK987 [17]3 years ago

4 0

Answer:

$x=-3\\\\y=-2$

Step-by-step explanation:

Given the system of equations $\left \{ {{-7x+6y=9} \atop {-2x-5y=16}} \right.$ , you can use the Elimination Method to solve it.

You can multiply the first equation by -2 and the second equation by 7, then add both equations and solve for the variable "y":

$\left \{ {{14x-12y=-18} \atop {-14x-35y=112}} \right.\\...........................\\-47y=94\\\\y=\frac{94}{-47}\\\\y=-2$

Substitute the value of "y" into any original equations and solve for the variable "x". Then:

$-7x+6y=9\\\\-7x+6(-2)=9\\\\-7x-12=9\\\\-7x=9+12\\\\x=\frac{21}{-7}\\\\x=-3$

Alex17521 [72]3 years ago

3 0

Answer:

x = -3 and y = -2

Step-by-step explanation:

It is given that,

-7x + 6y = 9 ----(1)

-2x - 5y = 16 -------(2)

<u>To find the solution of given equations</u>

eq(1) * 2 ⇒

-14x + 12y = 18 ------(3)

eq(2) * 7 ⇒

-14x - 35y = 112 ---(4)

eq (3) - eq(4) ⇒

-14x + 12y = 18 ------(3)

<u>-14x - 35y = 112 </u> ---(4)

0 4y = -94

y = 94/(-47) = -2

Substitute the value of y in eq (2)

-2x - 5y = 16 -------(2)

-2x - 5*-2 = 16

-2x +10 = 16

-2x = 6

x = 6/-2 = -3

Therefore x = -3 and y = -2

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Answer:

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 120 or not, the system of hypothesis would be:

Null hypothesis: $\mu = 120$

Alternative hypothesis: $\mu \neq 120$

Part 2

Calculate the statistic

We can replace in formula (1) the info given like this:

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P-value

Since is a two sided test the p value would be:

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Step-by-step explanation:

Data given and notation

$\bar X=114$ represent the sample mean

$\sigma=22$ represent the population standard deviation

$n=36$ sample size

$\mu_o =120$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part 1

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 120 or not, the system of hypothesis would be:

Null hypothesis: $\mu = 120$

Alternative hypothesis: $\mu \neq 120$

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part 2

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{114-120}{\frac{22}{\sqrt{36}}}=-1.636$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z$

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