SOLUTION: hi, could u please help me with this question.. the X^2 + Y^2 has throw me off! Q. Solve for x and y the equations.. x+2y=6 x^2+y^2=17 Many Thanks :)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: hi, could u please help me with this question.. the X^2 + Y^2 has throw me off! Q. Solve for x and y the equations.. x+2y=6 x^2+y^2=17 Many Thanks :)      Log On


   

Question 774225: hi, could u please help me with this question.. the X^2 + Y^2 has throw me off!
Q. Solve for x and y the equations..
x+2y=6
x^2+y^2=17
Many Thanks :)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this by substitution
+x+%2B+2y+=+6+
+x+=+6+-+2y+
-------------
+x%5E2+%2B+y%5E2+=+17+
+%28+6+-+2y+%29%5E2+%2B+y%5E2+=+17+
+36+-+24y+%2B+4y%5E2+%2B+y%5E2+=+17+
+5y%5E2+-+24y+%2B+19+=+0+
+y+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+5+
+b+=+-24+
+c+=+19+
+y+=+%28-%28-24%29+%2B-+sqrt%28+%28-24%29%5E2+-+4%2A5%2A19+%29%29+%2F+%282%2A5%29+
+y+=+%28+24+%2B-+sqrt%28+576+-+380+%29%29+%2F+10+
+y+=+%28+24+%2B-+sqrt%28+196+%29%29+%2F+10+
+y+=+%28+24+%2B-+14%29+%2F+10+
+y+=+38%2F10+
+y+=+3.8+
and
+y+=+10%2F10+
+y+=+1+
------------
Plug these results back into either equation
+x+%2B+2y+=+6+
+x+%2B+2%2A3.8+=+6+
+x+%2B+7.6+=+6+
+x+=+-1.6+
So you have the point ( -1.6, 3.8 )
and, plugging in +y+=+1+
+x+%2B+2y+=+6+
+x+%2B+2%2A1+=+6+
+x+=+4+
This is the point ( 4,1 )
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Here's the plot: