Page 11 - 10th maths -1

Simultaneous linear equations

When we think about two linear equations in two variables at the same
time, they are called simultaneous equations.
Last year we learnt to solve simultaneous equations by eliminating one

variable. Let us revise it.
Ex. (1) Solve the following simultaneous equations.

(1) 5x - 3y = 8; 3x + y = 2

Solution :
Method (II)
Method I : 5x - 3y = 8. . . (I)
5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
3x + y = 2 . . . (II)
Multiplying both sides of
Let us write value of y in terms
equation (II) by 3. of x from equation (II) as

9x + 3y = 6 . . . (III) y = 2 - 3x . . . (III)

5x - 3y = 8. . . (I) Substituting this value of y in

Now let us add equations (I) equation (I).

and (III) 5x - 3y = 8

5x - 3y = 8 \ 5x - 3(2 - 3x) = 8
+
9x + 3y = 6 \ 5x - 6 + 9x = 8

14x = 14 \ 14x - 6 = 8

\ x = 1 \ 14x = 8 + 6

substituting x = 1 in equation (II) \ 14x = 14

3x + y = 2 \ x = 1

\ 3 ´ 1 + y = 2 Substituting x = 1 in equation

\ 3 + y = 2 (III).

\ y = -1 y = 2 - 3x

solution is x = 1, y = -1; it is also \ y = 2 - 3 ´ 1

written as (x, y) = (1, -1) \ y = 2 - 3

\ y = -1

x = 1, y = -1 is the solution.

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