Help for 2 Unknowns

• Equation Set Up
  • Set up 2 equations x = amount invested at 6% and    y = amount invested at 7%. 
  • .06x + .07y = 270     and     x + y = 4000
  • use one of the methods below to solve for the 2 unknowns
•  .Solving for 2 Unknowns using the Substitute Method
  • Example: 3x +2y = 2   and     x + y = 4
  • Solve for one variable in terms of the other.
    x - x + y = 4 - x subtracted x from both sides y = 4 - x
  • Substitute this value of y, (y = 4 - x) in the second equation.
    3x + 2(4 - X) = 2
  • Solve: 3x + 2(4 - X) = 2   3x + 8 - 2x = 2   x+ 8 = 2    x = - 6
  • Substitute this value (x = -6) in the first equation and solve for the other variable
     x + y = 4         -6 + y = 4         y = 10
  •  Check
    x + y = 4      -6 + 10 = 4            4 = 4
  • Answer    x = -6  and y = 10

• Solving for 2 Unknowns using the Add and Subtrtact Method
  • Example :  6x + y =20     x + y= 10
  • Add or subtract the 2 equations to eliminate one of the variables.
    In our example we will subtract. This will eliminate the y's
  • 6x + y =20
    - x + y= 10
       5x = 10
  • Solve: 5 x = 10           x =2
  • Substitute: the value for x in the first equation and solve for y.
  • 6(2) + y = 20
  • 12 + y = 20   subtract 12 from both sides  y = 8
  • Check
    x + y = 10       2 + 8 = 10        10 = 10

   

  
   

  
  
  
  
  
   

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