4.1 Simultaneous Equations


4.1 Simultaneous Equations

(A) Steps in solving simultaneous equations:

  1. For the linear equation, arrange so that one of the unknown becomes the subject of the equation.
  2. Substitute the linear equation into the non-linear equation.
  3. Simplify and expressed the equation in the general form of quadratic equation a x 2 + b x + c = 0
  4. Solve the quadratic equation. 
  5. Find the value of the second unknown by substituting the value obtained into the linear equation.


Example:
Solve the following simultaneous equations.
y + x = 9 x y = 20 Solution:
For the linear equation, arrange so that one of the unknown becomes the subject of the equation.
y + x = 9 y = 9 x Substitute the linear equation into the non-linear equation.
x y = 20 x ( 9 x ) = 20 9 x x 2 = 20 Simplify and expressed the equation in the general form of quadratic equation a x 2 + b x + c = 0
9 x x 2 = 20 x 2 9 x + 20 = 0 Solve the quadratic equation. 
x 2 9 x + 20 = 0 ( x 4 ) ( x 5 ) = 0 x = 4  or  x = 5 Find the value of the second unknown by substituting the value obtained into the linear equation.
When  x = 4 , y = 9 x = 9 4 = 5 When  x = 5 , y = 9 x = 9 5 = 4

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