SOLUTION: Hi, please help me solve this by substitution method. Thank you! {{{ 2x+y=5 }}} {{{ x^2+y^2=50 }}}

Algebra ->  Systems-of-equations -> SOLUTION: Hi, please help me solve this by substitution method. Thank you! {{{ 2x+y=5 }}} {{{ x^2+y^2=50 }}}      Log On


   

Question 1061540: Hi, please help me solve this by substitution method. Thank you!
+2x%2By=5+
+x%5E2%2By%5E2=50+
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
The linear equation will give you y%5E2=%285-2x%29%5E2=25-20x%2B4x%5E2 to use as a direct substitute.

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, please help me solve this by substitution method. Thank you!
+2x%2By=5+
+x%5E2%2By%5E2=50+
2x + y = 5_____y = 5 - 2x ----- eq (i)

x%5E2+%2B+y%5E2+=+50 -------- eq (ii)

x%5E2+%2B+%285+-+2x%29%5E2+=+50 ------ Substituting 5 - 2x for y in eq (ii)

x%5E2+%2B+25+-+20x+%2B+4x%5E2+=+50

5x%5E2+-+20x+%2B+25+-+50+=+0



(x - 5)(x + 1) = 0 --- Factoring trinomial

highlight%28matrix%281%2C7%2C+x%2C+%22=%22%2C+5%2C+or%2C+x%2C+%22=%22%2C+-+1%29%29



y = 5 - 2(5) --------- Substituting 5 for x in eq (i)

highlight%28matrix%281%2C7%2C+y%2C+%22=%22%2C+5+-+10%2C+or%2C+y%2C+%22=%22%2C+-+5%29%29



y = 5 - 2(- 1) ------- Substituting - 1 for x in eq (i)

highlight%28matrix%281%2C7%2C+y%2C+%22=%22%2C+5+%2B+2%2C+or%2C+y%2C+%22=%22%2C+7%29%29