SOLUTION: Please help me solving this quadratic equation system: {{{ x^2+2*x-y+4=0 }}} {{{ 3*x-y+6=0 }}}

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Question 1086830: Please help me solving this quadratic equation system:
+x%5E2%2B2%2Ax-y%2B4=0+
+3%2Ax-y%2B6=0+

Found 3 solutions by Fombitz, MathTherapy, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Line intersecting a parabola,
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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me solving this quadratic equation system:
+x%5E2%2B2%2Ax-y%2B4=0+
+3%2Ax-y%2B6=0+
x%5E2+%2B+2x+-+y+%2B+4+=+0 ------- eq (i)
3x - y + 6 = 0 ======> y = 3x + 6 ------ eq (ii)
x%5E2+%2B+2x+-+%283x+%2B+6%29+%2B+4+=+0 -------- Substituting 3x + 6 for y in eq (i)
x%5E2+%2B+2x+-+3x+-+6+%2B+4+=+0
x%5E2+-+x+-+2+=+0
(x - 2)(x + 1) = 0
x = 2 OR x = - 1
y = 3(2) + 6 ------- Substituting 2 for x in eq (ii)
y = 6 + 6, or 12

y = 3(- 1) + 6 ------- Substituting - 1 for x in eq (ii)
y = - 3 + 6, or 3

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
For many solved problems on systems of non-linear equations (that are samples to you) see the lessons
    - Solving the system of algebraic equations of degree 2 and degree 1
    - Solving the system of algebraic equations of degree 2
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of equations that are not linear".