Equation with two variables

Question

90y+55x=9545

and x+y=115

what is x & y??

Answer 1

If x+y = 115 then x=115-y ... Substitute: 90y+55(115-y)=9545=35y+6325. Solve for y = (9545-6325)/35=92. Use this answer and go back to the first equation and solve for x=115-92= 23.

Answer 2

rewrite your system with x first then y and last what they are equal such that

A x + By = C ; A,B,C are constants

thus we have

55x + 90y = 9545

1x + 1y = 115

Transforming Matrix to the reduced row echelon form

1 0 23

0 1 92

thus x = 23 & y = 92

Note Matrix to the reduced row echelon form encompasses substitution and elimination and other techniques and is much faster for bigger systems ( more powerful method ) and tells you more information i.e is your system consistent [ no solution , infinity many , or one ]