Simultaneous Linear Equations in two Variables –
Two linear equations in two unknowns x & y are said to form a system of simultaneous linear equations if each of them is satisfied by the same pair of values of x & y. The general form of a system of simultaneous linear equations in two variables is –
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Example.1) – Consider the system of linear equations x + y = 12, x – y = 8
By substitution, you will find that each of these equations is satisfied by the values x = 10, and y = 2. Hence, the two given equations form a system of simultaneous linear equations in x & y.