Chapter 4 Simultaneous Equations

Simultaneous equations in two unknowns, one linear equation and one non-linear equation, can be solved using the sudstitution method by following the steps below:

Step 1: arrange the linear equation so that one of the two unknowns become the subject of the equation.

Step 2: substitude the equation from step 1 into the non-linear equation, simplify and express it
in the form of :

ax^2 + bx + c = 0.


Step 3: Solve the quadratic equation using factorisation, completing the square, or using the
formula.

Step 4: Substitude the value of the unknown obtained in step 3 into the linear equation to find the value of the other unknown.

Example:

(1) y - 2x = 0
(2) x^2 + xy + 5x = 0

From (1) y = 2x ..................................................................(3)
Substitude (3) into (2) :

x^2 + x(2x) + 5x = 0
x^2 + 2x^2 + 5x = 0
3x^2 + 5x - 8 = 0
(3x + 8)(x - 1) = 0
3x + 8 = 0 or x - 1 = 0
x = -8/3 or x = 1

substitude x = -8/3 into (3) , y = 2 (-8/3)
= -16/3

substitude x = 1 into (3) , y = 2 (1)
= 2

the solution is: x = -8/3 , y = -16/3
x = 1 , y = 2