Solving the solution of two variables of system equation that leads to the word problems on simultaneous linear equations is the ordered pair (x, y) which satisfies both the linear equations. Up to now, we have solved equations with only one unknown variable. When solving for two unknown variables, two equations are required, and these equations are known as simultaneous equations. The solutions are the values of the unknown variables which satisfy both equations simultaneously. In general, if there are n unknown variables, then n independent equations are required to obtain a value for each of the n variables.
An example of a system of simultaneous equations is
4y + 3x = 100
4y – 19x = 12
We have two independent equations to solve for two unknown variables. We can solve simultaneous equations algebraically using substitution and elimination methods.
System of simultaneous linear equations
A pair of linear equations in the same two variables form a system of simultaneous linear equations
They are satisfied by the same pair of values of the two variables
Two linear equations can have either only one solution, no solution or infinite solutions
Main methods of solving simultaneous linear equations (SE)
(i) Substitution method (S)
(ii) Elimination method – Subtraction or Addition (E)