Question

Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.

Answer 1

The given equations are
7y - 3x = 7     ....(i)
5y - 11x = 87  ....(ii)
5x + 4y = 43  ....(iii)
Multiplying eqn. (i) by 5 and eqn. (ii) by 7, we get
35y - 15x = 35   ....(iv)
35y - 77x = 609 ....(v)
Subtracting eqn. (iv) from eqn. (v), we get
-62x = 574
⇒ x = `-(574)/(62) = -(287)/(31)`

⇒ `7y - 3x (-287/31)` = 7

⇒ `7y + (861)/(31)` = 7

⇒ 7y

= `7 - (861)/(31)`

= `(217 - 861)/(31)`

= `-(644)/(31)`

⇒ y = `-(644)/(7 xx 31)`

= `-(92)/(31)`
Putting x = `(-287)/(31) and y = `-(92)/(31)` in L.H.S. of eqn. (iii), we get

L.H.S. = `5 xx (-287/31) + 4x(-92/31)`

= `-(1435)/(31) - (368)/(31)`

= `-(1803)/(31)` ≠ 43

⇒ L.H.S. ≠ R.H.S.
Hence, the given system of equations are not consistent.