Question

solve for x and y : (i) 217x + 131y = 913 (ii) 131x + 217y = 827

Answer 1

217x + 131y:913 ........(1)
131x + 217y: 827 ........2
equation(1) * 131 and (2) *217 we get
67921x + 17161y: 119603
62921x +47089y: 179459
- - -
--------------------------------------
0 - 29928y: - 59856
29928y: 59856
y:59856/29928
y: 2
substituting value of y in equation (1) we get
217x + 131 * 2:913
217x + 262 :913
217x : 913- 262
217x :651
x: 651/217
x: 3
x:3; y:2 ANS

Answer 2

217 x + 131 y = 913 ----- ( 1 )

131 x + 217 y = 827 ----- ( 2 )

Now, multiply eq.(1) with 131 and eq(2) with 217
we get,

28427 x + 17161 y = 119603------(1a)
28427 x + 47089 y= 179459-----(2a)
Now substract eqs. (1a) and (2a)
we get -29928 y = -59856
y= -59856/-29928

y=2
Now substitute y=2 in eq.(1), we get

217 x + 131 (2) =913
217 x + 262 = 913
217 x=913-262
217 x=651
x=651/217
x=3
Therefore x=3 and y=2