# 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 $$a{x^2} + bx + c = 0$$
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.
$\begin{array}{l} y + x = 9\\ xy = 20 \end{array}$ Solution:
For the linear equation, arrange so that one of the unknown becomes the subject of the equation.
$\begin{array}{l} y + x = 9\\ y = 9 - x \end{array}$ Substitute the linear equation into the non-linear equation.
$\begin{array}{l} xy = 20\\ x(9 - x) = 20\\ 9x - {x^2} = 20 \end{array}$ Simplify and expressed the equation in the general form of quadratic equation $$a{x^2} + bx + c = 0$$
$\begin{array}{l} 9x - {x^2} = 20\\ {x^2} - 9x + 20 = 0 \end{array}$ Solve the quadratic equation.
Find the value of the second unknown by substituting the value obtained into the linear equation.