Question

Solve: 101x-99y=103 -99x+101y=-97

Answer 1

Answer:

$x=2; y=1$

Step-by-step 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.