Solve for y. 2x + 1/y = 3

Question

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Answer 1

Jennifer,

Solving for y means to get everything else to the other side of the equation, and y on one side of the equation.

 

2x + (1/y) = 3  ; y ≠ 0

Multiply both sides by y:

2xy +(1/y)y = 3y

2xy + 1 = 3y

Subtract 1 from both sides:

2xy + 1 - 1 = 3y - 1

2xy + (0) = 3y - 1

Subtract 3y from both sides:

2xy - 3y = 3y - 3y -1

2xy - 3y = (0) - 1

2xy - 3y = -1

Factor out y from the left:

y(2x - 3) = -1

Divide both sides by (2x - 3):

(y(2x-3))/(2x-3) = -1/(2x - 3)

y = -1/(2x - 3)

 

Because you have a variable in the denominator, you have to specify what value(s) the variable cannot possibly be.  

 

To do that, set the denominator equal to 0 and solve for the variable in the denominator (can't divide by 0):

2x - 3 = 0

Add 3 to both sides:

2x - 3 + 3 = 0 + 3

2x +(0) = 3

Divide both sides by 2:

2x/2 = 3/2

x = 3/2

 

Therefore the answer is:

 

y = -1/(2x -3)  ; x ≠ 3/2 ; y ≠ 0

Answer 2

2x + 1/y = 3               Assume that y ≠ 0, multiply both sides by "y."

 

2xy + 1 = 3y               Subtract 3y from both sides, subtract 1 from both sides

2xy - 3y = -1               Factor out the "y."

y(2x - 3) = -1              Divide both sides by (2x - 3)

y = -1 / (2x - 3)