Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of t
he system is 3y = 2x – 9. Which could be the other equation?
2 answers:
A system of equations with infinitely many solutions is a system where the two equations are identical. The lines coincide. Anything that is equal to 
will work. You could try multiply the entire equation by some number, or moving terms around, or adding terms to both sides, or any combination of operations that you apply to the entire equation.
You could multiply the whole thing by 4.5 to get
. If you want, you could mix things up and write it in slope-intercept form: 
. The point is, anything that is equivalent to the original equation will give infinitely many solutions x and y. You can test this by plugging in values x and y and seeing the answers!
The attached graph shows that four different equations are really the same.
You could multiply the whole thing by 4.5 to get
The attached graph shows that four different equations are really the same.
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Answer:
And we got so then the value for
and then the confidence level is given by:
represent the real population proportion for 1
represent the estimated proportion for 1
is the sample size required for 1
represent the real population proportion for 2
represent the estimated proportion for 2
is the sample size required for 2
represent the critical value for the margin of error
The population proportion have the following distribution
The confidence interval for the difference of two proportions would be given by this formula
For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:
And we know that the margin of erro is given by:
We have all the values except the value for
So we can find it like this:
And solving for we got:
And we can find the value for with the following excel code:
"=1-NORM.DIST(2.326,0,1,TRUE)"
And we got so then the value for
and then the confidence level is given by:
or 98%