LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SOLUTION 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 = 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 equatio****ns**.