Question

Find the ordered pair that is a member of both -2x + 6y = 34 and

2x + 2y = 14 or indicate if it does not exist or there are infinite
possibilities.

Answer 1

(1, 6) is the solution

Explanation:

-2x + 6y = 34

2x + 2y = 14; divide by 2

x + y = 7; subtract x

y = 7 - x

let's substitute y with 7 - x in first equation

-2x + 6*(7 - x) = 34; expand multiplication

-2x + 6*7 - 6*x = 34; group

-8x + 42 = 34; subtract 42

-8x = 34 - 42 = -8; divide by -8

x = 1

y = 7 - 1 = 6

It is the only solution, as we've arrived at exact numbers.