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3 years ago

(x+y,x-2y)=(4,1), find x and y

Mathematics

2 answers:

dimulka [17.4K]3 years ago

6 0

Answer:

x = 3, y = 1

Step-by-step explanation:

Equate the x and y coordinates of the given points

x + y = 4 → (1)

x - 2y = 1 → (2)

Subtract (2) from (1) term by term to eliminate x

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

y + 2y = 3

3y = 3 ( divide both sides by 3 )

y = 1

Substitute y = 1 into (1) for corresponding value of x

x + 1 = 4 ( subtract 1 from both sides )

x = 3

gtnhenbr [62]3 years ago

5 0

Answer:

x =3 and y =1

Step-by-step explanation:

( x+y , x-2y) = (4 , 1)

compare their corresponding elements

x+y = 4

y = 4 - x equation (i)

x-2y =1

substitute the value of x

x - 2(4 - x) =1

x - 8 + 2x =1

3x = 1 +8

x = 9/3

x = 3

Now substitute the value of x in equation (i)

y = 4 - x

y = 4 - 3

y = 1

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So on this case the 90% confidence interval would be given by (-0.30;2.50)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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$\bar X=1.1$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=51 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

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In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

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Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,50)".And we see that $t_{\alpha/2}=2.02$