2x+3y=34;7x*4y=342

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Solution for 2x+3y=34;7x*4y=342 system of equations: 


  • /| 2*x+3*y-34 = 0| 4*7*x*y-342 = 0
  • We try to solve the equation: 2*x+3*y-34 = 0
  • 2*x+3*y-34 = 0 // - 2*x-34
  • 3*y = -(2*x-34) // : 3
  • y = (-(2*x-34))/3
  • y = (34-(2*x))/3
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| 4*7*x*((34-(2*x))/3)-342 = 0| y = (34-(2*x))/3
  • (28*x*(34-2*x))/3-342 = 0
  • 952/3*x-56/3*x^2-342 = 0
  • 952/3*x-56/3*x^2-342 = 0
  • DELTA = (952/3)^2-(-342*(-56/3)*4)
  • DELTA = 676480/9
  • DELTA > 0, so the uquation has 2 solutions
  • x = ((676480/9)^(1/2)-952/3)/(-56/3*2) or x = (-(676480/9)^(1/2)-952/3)/(-56/3*2)
  • x = -3/112*((676480/9)^(1/2)-952/3) or x = 3/112*((676480/9)^(1/2)+952/3)
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = -3/112*((676480/9)^(1/2)-952/3)
  • For y = (34-(2*x))/3: 
  • y = (34-(-3/112*2*((676480/9)^(1/2)-952/3)))/3
  • y = (34-(-3/56*((676480/9)^(1/2)-952/3)))/3
  • We get a system of equations:
  • /| y = (3/56*((676480/9)^(1/2)-952/3)+34)/3| x = -3/112*((676480/9)^(1/2)-952/3)
  • 2) For x = 3/112*((676480/9)^(1/2)+952/3)
  • For y = (34-(2*x))/3: 
  • y = (34-(3/112*2*((676480/9)^(1/2)+952/3)))/3
  • y = (34-(3/56*((676480/9)^(1/2)+952/3)))/3
  • We get a system of equations:
  • /| y = (34-3/56*((676480/9)^(1/2)+952/3))/3| x = 3/112*((676480/9)^(1/2)+952/3)

 

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