What is the value of y in the solution to the system of equations 1/3x+1/4y=1

We think you wrote:

This solution deals with linear equations with two unknowns.

  [1] x/3 + y/4 = 1   [2] 2x - 3y = -30

// To remove fractions, multiply equations by their respective LCD

     Multiply equation [1] by 12

// Equations now take the shape:

  [1] 4x + 3y = 12   [2] 2x - 3y = -30

Graphic Representation of the Equations :

3y + 4x = 12 -3y + 2x = -30

Solve by Substitution :

// Solve equation [2] for the variable  x 
 

[2] 2x = 3y - 30 [2] x = 3y/2 - 15

// Plug this in for variable  x  in equation [1]

  [1] 4•(3y/2-15) + 3y = 12   [1] 9y = 72

// Solve equation [1] for the variable  y 

  [1] 9y = 72    [1] y = 8 

// By now we know this much :

  x = 3y/2-15   y = 8

// Use the  y  value to solve for  x 

  x = (3/2)(8)-15 = -3 

Solution :

 {x,y} = {-3,8} 


Page 2

We think you wrote:

This solution deals with linear equations with two unknowns.

  [1] x/3 + y/4 = 1   [2] 2x - 3y = -30

// To remove fractions, multiply equations by their respective LCD

     Multiply equation [1] by 12

// Equations now take the shape:

  [1] 4x + 3y = 12   [2] 2x - 3y = -30

Graphic Representation of the Equations :

3y + 4x = 12 -3y + 2x = -30

Solve by Substitution :

// Solve equation [2] for the variable  x 
 

[2] 2x = 3y - 30 [2] x = 3y/2 - 15

// Plug this in for variable  x  in equation [1]

  [1] 4•(3y/2-15) + 3y = 12   [1] 9y = 72

// Solve equation [1] for the variable  y 

  [1] 9y = 72    [1] y = 8 

// By now we know this much :

  x = 3y/2-15   y = 8

// Use the  y  value to solve for  x 

  x = (3/2)(8)-15 = -3 

Solution :

 {x,y} = {-3,8} 

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