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solving a system of 2 equations with 2 variables











































write equation for sum of reciprocals

One number is 2 times another.

Write an expression for the sum of their reciprocals.

Simplify the expression. (Use x for the variable.)

Comments for solving a system of 2 equations with 2 variables

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May 05, 2014
sum of reciprocals
by: Staff


Answer

Part I

x = 1st number

z = 2nd number

y = sum of the reciprocals

y = (1/x) + (1/z)


Definitions – sum of reciprocals





z = 2x



substitute 2x for z


y = (1/x) + (1/(2x))


substitution method - substitute 2x for z







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May 05, 2014
sum of reciprocals
by: Staff


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Part II


multiply each side of the equation by 2x


2x * y = 2x * [(1/x) + (1/(2x))]


Expand using the distributive law

2x * y = 2x * [(1/x) + (1/(2x))]

2xy = (2x / x) + (2x / (2x))


multiply each side of the equation by 2x, and then apply the distributive law





Simplify the right side of the equation by cancelling like terms

2xy = 2 + 1

2xy = 3


cancel the like terms in the numerator and denominator for each fraction








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May 05, 2014
sum of reciprocals
by: Staff


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Part III


Divide by 2x

2xy / (2x) = 3 / (2x)

y = 3 / (2x)

y = 1.5 / x


divide both sides of the equation by 2x





the final answer is:

y = 1.5 / x, x ≠ 0



sum of reciprocals – final answer






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May 05, 2014
sum of reciprocals
by: Staff


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Part IV



the graph of the sum of two reciprocals is a hyperbola








Thanks for writing.

Staff
www.solving-math-problems.com


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