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2 years ago

3x-4y=1 and x=2y+1 using substitution

Mathematics

1 answer:

Aleksandr [31]2 years ago

3 0

Answer:

x =-1

y =-1

Step-by-step explanation:

to solve this system of equation, using substiution method

3x-4y=1 ........................ equation 1

x=2y+1 ............................ equation 2

subbstitute for x into equation 1

3x-4y=1 ........................ equation 1

3(2y + 1) - 4y = 1

6y + 3 -4y = 1

2y + 3 = 1

collect the like terms

2y = 1- 3

2y= -2

divide both sides by the coefficient of y which is y

2y/2 = -2/2

y = -1

put the value of y =-1 into equation 2

x=2y+1 ............................ equation 2

x = 2(-1) + 1

x = -2 + 1

x = -1

therefore x =-1 y = -1

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Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=35$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s =2.12$ represent the sample deviation obtained

$\sigma_0 =3$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is lower than 9 and the deviation lower than 3, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \geq 9$

Alternative hypothesis: $\sigma^2$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

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Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df= n-1= 35-1=34. And since is a left tailed test the p value would be given by:

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(16.979,34,TRUE)"

Conclusion

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