# CLASS-9SOLUTION OF TWO SIMULTANEOUS LINEAR EQUATIONS

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 = 16R.H.S

Thus, the values x = 4, and y = 2 do not satisfy (2)

Hence, x = 4y = 2 is not a solution of the given system of equations.