Question

Factorise: by elimination of coefficient 13x+11y=70 11x+13y=74

Answer 1

GIVEN:-

13x+11y=70.............(1)

11x+13y= 74...........(2)

To find solution of x and y

SOLUTION:-

eqn(1)×11 - eqn(2)×13

=> 121y-169y = 70²-74²..[ a²-b²=(a+b)(a-b)]

=> 48y = 4×144

=> y = 4×144/48 = 12

substituting in eqn(1)

13x+11×12 = 70

=> 13x = 70-132= -52

=> x = -4

Therefore, x = -4 and y = 12

hope this helps you

Answer 2

$13x + 11y = 70 \: \: \: .......(i)$

$11x + 13y = 74 \: \: \: .........(ii)$

Adding (i) and (ii), we get,

$24x + 24y = 144$

Or,

$x + y = 6 \: \: \: ......(iii)$

Subtracting (ii) from (i), we get,

$2x - 2y = - 4$

Or,

$x - y = - 2 \: \: \: .....(iv)$

Adding (iii) and (iv), we get,

$2x = 4$

Or,

$x = 2$

Therefore,

$y = 6 - x$

$= 6 - 2$

$= 4$

Answer:-

$x = 2$

$y = 4$