document.write( "Question 884679: Solving quadratic systems. Also asked to state which conic section each equation represents. (Circle, parabolas, etc). Please explain how to solve 4x^2+9y^2=144
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Algebra.Com's Answer #534558 by MathTherapy(10552)\"\" \"About 
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Solving quadratic systems. Also asked to state which conic section each equation represents. (Circle, parabolas, etc). Please explain how to solve 4x^2+9y^2=144
\n" ); document.write( " 2x+3y=12 either by elimination or substitution. Also advise how would I know which conic section to chose.
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document.write( "\"4x%5E2+%2B+9y%5E2+=+144\"
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document.write( "Since the coefficients (4 & 9) on the 2nd degree variables are UNEQUAL, this conic section is an ELLIPSE.\r
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document.write( "\"2x+%2B+3y+=+12\"
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document.write( "First degree variables exist, so a LINEAR EQUATION, thus a LINE graph.\r
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document.write( "\"4x%5E2+%2B+9y%5E2+=+144\" -------- eq (i)
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document.write( "2x + 3y = 12______2x = 12 - 3y____\"x+=+%2812+-+3y%29%2F2\" -------- eq (ii)
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document.write( "\"4%28%2812+-+3y%29%2F2%29%5E2+%2B+9y%5E2+=+144\" --------- Substituting \"%2812+-+3y%29%2F2\" for x in eq (i)
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document.write( "\"4%28%28144+-+72y+%2B+9y%5E2%29%2F4%29+%2B+9y%5E2+=+144\"
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document.write( "\"cross%284%29%28%28144+-+72y+%2B+9y%5E2%29%2Fcross%284%29%29+%2B+9y%5E2+=+144\"
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document.write( "\"144+-+72y+%2B+9y%5E2+%2B+9y%5E2+=+144\"
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document.write( "\"18y%5E2+-+72y+%2B+144+-+144+=+0\"
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document.write( "\"18y%5E2+-+72y+=+0\"
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document.write( "\"18y%28y+-+4%29+=+0\"
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document.write( "\"highlight_green%28highlight_green%28y+=+4_or_y+=+0%29%29\"\r
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document.write( "2x + 3(4) = 12 -------- Substituting 4 for y in eq (ii)
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document.write( "2x + 12 = 12
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document.write( "2x = 0
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document.write( "\"x+=+0%2F2\", or \"x++=+0\"\r
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document.write( "2x + 3(0) = 12 -------- Substituting 0 for y in eq (ii)
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document.write( "2x + 0 = 12
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document.write( "2x = 12
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document.write( "\"x+=+12%2F2\", or \"x++=+6\"
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document.write( "\"highlight_green%28highlight_green%28x+=+0_or_x+=+6%29%29\"\r
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document.write( "Therefore, \"highlight_green%28highlight_green%28x+=+0_when_y+=+4%29%29\" and \"highlight_green%28highlight_green%28x+=+6_when_y+=+0%29%29\"
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document.write( "You can do the check!! \r
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document.write( "If you need a complete and detailed solution, let me know!!\r
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document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
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document.write( "Further help is available, online or in-person, for a fee, obviously. \r
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