Solution of a given System of two Simultaneous Linear Equations –
A pair of values of x & y satisfying each of the equations in a given system of two simultaneous linear equations in x & y is called a solutions of the system.
Example.1) Show that x = 8, and y = 5 is a solution of the system of linear equations 3x – 2y = 14, x + 2y = 18
Ans.) The given equations are –
3x – 2y = 14………………. (1)
x + 2y = 18……………….. (2)
putting x = 8, and y = 5 in (1), we get
L.H.S = (3 X 8) – (2 X 5) = 24 – 10 = 14 = R.H.S
Putting x = 8, and y = 5 in (2), we get
L.H.S = (1 X 8) + (2 X 5) = 8 + 10 = 18 = R.H.S
Thus, x = 8, and y = 5 satisfy both (1) & (2)
Hence, x = 8, y = 5 is a solution of the given system of equations.
Example.2) Show that, x = 4, y = 2 is not a solution of the system of linear equations 5x – 7y = 6, 3x + 2y = 12.
Ans.) The equations are –
5x – 7y = 6…………….(1)
3x + 2y = 12………………….(2)
Putting x = 4, and y = 2 in (1), we get –
L.H.S = 5x – 7y = (5 X 4) – (7 X 2) = 20 – 14 = 6 = R.H.S
Putting x = 4, and y = 2 in (2), we get –
L.H.S = (3 X 4) + (2 X 2) = 12 + 4 = 16 ≠ R.H.S
Thus, the values x = 4, and y = 2 do not satisfy (2)
Hence, x = 4, y = 2 is not a solution of the given system of equations.