asked 129k views
25 votes
Solve: 101x-99y=103
-99x+101y=-97

1 Answer

9 votes

Answer:


x=2; y=1

Explanation:

Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.


I+II: 2x+2y=6\\I-II:200x-200y=200

Better, now let's simplify the expression and let's use the new system


x+y=3\\x-y=1

Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get
x=2, y=1 which, if you check by replacing in the original, is indeed a valid solution.

answered
User Ki
by
8.6k points
Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.