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Marizza181 [45]
3 years ago
15

Solve equation 3x-5y=7 5x-2y=-1 by elimination

Mathematics
2 answers:
kakasveta [241]3 years ago
7 0

Answer:

x = -1, y = -2.

Step-by-step explanation:

Using the elimination method,

multiply the first eqn by 2 and the 2nd eqn by 5.

6x - 10y = 14

25x - 10y = -5

Subtract one of the new equations from the other

-19x = 19

x = -1

Sub x=-1 into the 2nd eqn

-5 - 2y = -1

y = -2

Hence x = -1, y = -2.

jarptica [38.1K]3 years ago
5 0

Answer: x= -1, y= -2

Step-by-step explanation:

Multiply both sides of the equation by -2.

-6x + 10y= -14

5x - 2y= -1

Sum the equations vertically to eliminate at least one variable.

19x= -19

Divide both sides of the equation by 19.

x=-1

Substitute the given value of x into the equation 5x (-1) - 2y= -1.

Solve the equation for y.

y=-2

The possible solution of the system is the ordered pair (x,y)

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Alternative hypothesis:\mu < 250  

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If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not significantly lower than 530 at 5% of significance.      

Step-by-step explanation:

1) Data given and notation        

\bar X=510 represent the mean for the sample    

s=50 represent the standard deviation for the sample  

n=16 sample size        

\mu_o =530 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)    

2) State the null and alternative hypotheses.        

We need to conduct a hypothesis in order to determine if the claim thet the handle on average is 530 bags per hour:      

Null hypothesis:\mu \geq 530        

Alternative hypothesis:\mu < 530        

We don't know the population deviation and the sample size is lees than 30, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:        

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

t-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".    

3) Calculate the statistic        

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

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4) Calculate the critical value

We need to begin calculating the degrees of freedom

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The critical value for this case would be :

P(t_{15}

The value of a that satisfy this on the normal standard distribution is a=-1.75 and would be the critical value on this case zc=-1.75

5) Calculate the P-value        

Since is a one-side upper test the p value would be:        

p_v =P(t_{15}    

6) Conclusion        

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not significantly lower than 530 at 5% of significance.      

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