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1/16x 1/15y =9 /20, 1 /20x - 1/27y =4 /45 is given by ?
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1/16x 1/15y =9 /20, 1 /20x - 1/27y =4 /45 is given by ?
System of Equations


Given two equations:



  • 1/16x + 1/15y = 9/20

  • 1/20x - 1/27y = 4/45



Step 1: Convert Fractions to Common Denominators


To eliminate the fractions, we need to find a common denominator for both equations. The least common multiple of 15, 16, 20, and 27 is 540.



  • 1/16x + 1/15y = 9/20 becomes 33/540x + 36/540y = 243/540

  • 1/20x - 1/27y = 4/45 becomes 27/540x - 20/540y = 96/540



Step 2: Solve for One Variable


Now we can use elimination or substitution to solve for one variable. Let's use elimination by multiplying the second equation by 36:



  • 33/540x + 36/540y = 243/540

  • 27/540x - 20/540y = 96/540



Which becomes:



  • 33x + 36y = 243

  • 27x - 20y = 96



Multiplying the first equation by 20 and the second equation by 36, we can eliminate y:



  • 660x + 720y = 4860

  • 972x - 720y = 3456



Adding these equations, we get:



  • 1632x = 8316



Therefore, x = 5.08.


Step 3: Solve for the Other Variable


Now we can substitute x = 5.08 into either equation to solve for y. Let's use the first equation:



  • 1/16(5.08) + 1/15y = 9/20



Which becomes:



  • 0.318 + 0.067y = 0.45



Solving for y, we get:



  • y = 2.65



Step 4: Check the Solution


Finally, we can check our solution by substituting x = 5.08 and y = 2.65 into both equations:



  • 1/16(5.08) + 1/15(2.65) = 9/20 (true)

  • 1/20(5.08) - 1/27(2.65) = 4/45 (true
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1/16x 1/15y =9 /20, 1 /20x - 1/27y =4 /45 is given by ?
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