Question 572588: solve by elimination
6x-9y=13.5
7y-3x=-8
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! I'm going to guess here on what your "elimination" term means, only because I hate leaving you high and dry.
6x - 9y = 13.5 (I already hate this one btw)
7y - 3x = -8
First thing we're going to do is line up the x's and y's since they were too lazy to do that for you:
6x - 9y = 13.5 (unchanged)
-3x+ 7y = -8 (reversed the first two terms)
Now if we multiply the 2nd equation (both sides) by 2, we have something interesting in the x column:
2(-3x + 7y) = 2(-8)
-6x + 14y = -16
Rewriting the two equations with this change:
6x - 9y = 13.5 (unchanged again)
-6x + 14y = -16
What you'll notice is if we add these two equations vertically, the x factors cancel out so we get:
0 -9y + 14y = 13.5 - 16
5y = -2.5
Divide both sides by 5
y = -.5
But we still need x:
6x - 9(-.5) = 13.5 Multiplying the 9 by .5 and signs cancel:
6x + 4.5 = 13.5
Subtract 4.5 from both sides leaving:
6x = 9
x = 9/6 = 3/2 = 1.5 (did they have to?? I like whole numbers myself ;-)
Checking:
Equation 1:
6(1.5)-9(-.5) = 13.5
9 + 4.5 = 13.5 (you'll want to do this step for yourself, but all I did was multiply)
13.5 = 13.5 Correct!
Equation 2:
7(-.5) - 3(1.5) = -8
-3.5 - 4.5 = -8
-8 = -8 Correct!
Good luck! And please leave me feedback if I was correct in the definition of "elimination". :-)
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