Please solve for x & y in this equal matrix?

Question

|3x + y | |x + 3|

|x - 2y| = |y - 2|

Answer 1

3x+y = x+3

x-2y = y-2

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2x + y = 3 <--- subtracts x from both sides in first equation

x-3y = -2 <--- subtracts y from both sides in second equation

x = 3y-2 <--- solves second equation for x; please label this equation ALPHA

2(3y-2) + y = 3 <--- substitutes into first equation

6y - 4 + y = 3 <--- distributive

7y - 4 = 3 <--- combines like terms

7y = 7 <--- adds 4 to both sides

y=1 <-- divides both sides by 7

x = 3y-2 = 3(1)-2 = 3-2 = 1 <--- substitutes into equation ALPHA in bold above.

(1,1) is one solution