2x + 3y = 31
3x - y = 30
If (x,y) is the solution to the system of equations above, what is the value of 100x + 40y ?

The correct answer is: 1220

Hint:-
We solve the given equations simultaneously to find the value of x & y and then 100x + 40y.
Step-by-step solution:-
2x + 3y = 31 --------- (Equation i)
3x - y = 30 ------------ (Equation ii)
Multiplying equation ii by 3, we get-
9x - 3y = 90 ------------- (Equation iii)
Adding equations i & iii, we get-
2x + 3y = 31
(+) 9x - 3y = 90
11x = 121
∴ x = ---------- (Dividing both sides by 11)
∴ x = 11 -------------- (Equation iv)
Substituting Equation iv in Equation ii, we get-
3x - y = 30
3(11) - y = 30
∴ 33 - y = 30
∴ - y = 30 - 33
∴ - y = - 3
∴ y = 3 ------------- (Equation v)
Substituting values of x & y in 100x + 40y, we get-
100 x + 40 y = 100 (11) + 40 (3) -------------------- (From equations iv & v)
= 1,100 + 120
= 1,220
Final Answer:-
∴ The value of 100 x + 40 y is 1,220 for the above equations.