Question

x+y/xy = 3 ; x-y/xy = 1​

Answer 1

Step-by-step explanation:

We're given a system of two linear equations in two unknowns, x and y. We'll use the Addition/Subtraction method, also known as the Elimination method, to first solve the given system of equations for x and y so that we can in turn determine the ratio x/y.

Now, add the second equation x - y = 1 to the first equation x + y = 3 as follows:

x + y = 3

x - y = 1

---------

2x + 0y = 4

2x = 4

(2x)/2 = 4/2

x = 2

NOTE: We can add one equation to another because of the axiom: "If equals are added to equals, the sums are equal."¹

Now, substitute the value of x = 2 into either equation to find y. We'll choose the first one:

x + y = 3

2 + y = 3

2 - 2 + y = 3 - 2

0 + y = 1

y = 1

CHECK (in both equations!):

x + y = 3

2 + 1 = 3

3 = 3

x - y = 1

2 - 1 = 1

1 = 1

Therefore, the solution to the given system of linear equations is indeed x = 2 and y = 1; therefore, ...

x/y = 2/1

= 2

¹ Donald S. Russell. ALGEBRA PROBLEMS: A Portable Blackboard of Basic Principles With Step-by-Step Solutions; Barnes & Noble, Inc.; New York, New York, third printing, 1962, p. 22.

Answer 2

Answer:

3xy= x+y

xy= x-y

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