Can the following equations hold simultaneously?

3x - 7y = 7

11x + 5y = 87

5x + 4y = 43.

If so, find x and y.

Given,

3x - 7y = 7 ……..(i)

11x + 5y = 87 …….(ii)

5x + 4y = 43 …….(iii)

Solving first two equations simultaneously,

Multiplying eq. (i) by 11 and eq. (ii) by 3 we get,

33x - 77y = 77 ……(iv)

33x + 15y = 261 ……(v)

Subtracting eq. (iv) from (v) we get,

⇒ 33x + 15y - (33x - 77y) = 261 - 77

⇒ 33x - 33x + 15y + 77y = 184

⇒ 92y = 184

⇒ y = 2.

Substituting value of y in eq. (i) we get,

⇒ 3x - 7y = 7

⇒ 3x - 7(2) = 7

⇒ 3x - 14 = 7

⇒ 3x = 21

⇒ x = 7.

Substituting x = 7 and y = 2 in L.H.S. of eq. (iii),

5x + 4y = 43 …….(iii)

⇒ 5(7) + 4(2) = 35 + 8 = 43.

Since, L.H.S. = R.H.S. hence following equations can be held simultaneously.

Hence, x = 7 and y = 2.