SOLUTION: LINEAR SYSTEMS ALGEBRA; 7X-3Y=-23, X+5Y=32; AM TRYING TO HELP MY GRANDSON AND HAVE NO IDEA WHERE TO START. THINK I HAVE DONE ONE CORRECTLY X-Y=3, 2X-2Y=6 (I BELIEVE X = 4 AND Y

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Question 579050: LINEAR SYSTEMS ALGEBRA; 7X-3Y=-23, X+5Y=32; AM TRYING TO HELP MY GRANDSON AND HAVE NO IDEA WHERE TO START.
THINK I HAVE DONE ONE CORRECTLY X-Y=3, 2X-2Y=6 (I BELIEVE X = 4 AND Y = 1 BUT DO NOT HAVE ANY IDEA HOW TO SHOW THE WORK;
PLEASE AND THANK YOU
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the one you have done "correctly" works for any values of x and y, as long as x is 3 greater than y
___ there is no unique solution
___ this is the case when you can multiply one equation by a constant and get the other equation

x + 5y = 32 ___ x = 32 - 5y ___ substitute this equivalent value for x into the other equation

7(32 - 5y) - 3y = -23 ___ 224 - 35y - 3y = -23 ___ 247 = 38y ___ 247 / 38 = y ___ 13 / 2 = y

x + 5(13 / 2) = 32 ___ x + (65 / 2) = 64 / 2 ___ x = -1 / 2