SOLUTION: please help me figure it out #55 use substitution method 5x+2y=4 x=61-9y

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Question 515386: please help me figure it out #55 use substitution method
5x+2y=4
x=61-9y
Answer by drcole(72) About Me  (Show Source):
You can put this solution on YOUR website!
Since the second equation is already solved for x, we can substitute its right hand side for x in the first equation and get a new equation involving only y:
5x+%2B+2y+=+4
+5%2861+-+9y%29+%2B+2y+=+4 (substituting 61 - 9y for x)
Now we solve for y:
+305+-+45y+%2B+2y+=+4 (distributing 5 on the left side)
+305+-+43y+=+4 (combining like terms)
+-43y+=+-301 (subtracting 305 from both sides)
+y+=+7+ (divide both sides by -43)
So y = 7. To get x, we now substitute 7 for x in the first equation:
+x+=+61+-+9y+=+61+-+9%287%29+=+61+-+63+=+-2
SO our solution is x = -2 and y = 7. Let's check this. For the first equation, we get
5x+%2B+2y+=+5%28-2%29+%2B+2%287%29+=+-10+%2B+14+=+4
so that works. For the second equation, we get:
+x+=+61+-+9y
-2+=+61+-+9%287%29
+-2+=+61+-+63
which also works. So x = -2 and y = 7 is the correct solution.