Linear Equation 19

Solve the following system of equations by the method of elimination by substitution:

(i) 2 x + 3 y = 7

3 x - y = 5

(ii) x + 11 y = 1

8 x + 13 y = 2

Solution:

3 x - y = 5 => 3 x - 5 = y ; i.e. y = 3 x - 5

2 x + 3 y = 7 => 2 x + 3 ( 3 x - 5) = 7

=> 2 x + 9 x - 15 = 7

=> 11 x = 22 ; i.e. x = 2

y = 3 x - 5 => y = 3 X 2 - 5 = 1

Therefore, Solution is : x = 2 and y = 1

(ii) x + 11 y = 1 => x = 1 - 11 y

8 x + 13 y = 2 => 8 (1 - 11 y) + 13 y = 2

=> 8 - 88 y + 13 y = 2

=> - 75 y = - 6

i.e. y = - 6 / - 75 = 2 / 25

x = 1 - 11 y => x = 1 - 11 X 2 / 25 = ( 25 - 22 ) / 25 = 3 / 25

Therefore, the solution is: x = 3 / 25 and y = 2 / 25