document.write( "Question 931571: Solve algebraically
\n" ); document.write( "4x^2+y^2=64
\n" ); document.write( "×^2+y^2=52 \n" ); document.write( "

Algebra.Com's Answer #565620 by Theo(13342) $\"\"$ $\"About$

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this can be solved graphically as shown in the following picture.\r
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\n" ); document.write( "\n" ); document.write( "but, you wanted an algebraic solution.
\n" ); document.write( "now we'll work on that.\r
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\n" ); document.write( "\n" ); document.write( "you have the 2 equations you started out with.
\n" ); document.write( "they are:\r
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\n" ); document.write( "\n" ); document.write( "x^2 + y^2 = 52 (first equation)
\n" ); document.write( "4x^2 + y^2 = 64 (second equation)\r
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\n" ); document.write( "\n" ); document.write( "we can solve by elimination to find the value of x^2.
\n" ); document.write( "once we find the value of x^2, we can then find the value of y^2.\r
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\n" ); document.write( "\n" ); document.write( "subtract the first equation from the second equation to get:\r
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\n" ); document.write( "\n" ); document.write( "4x^2 - x^2 + y^2 - y^2 = 64 - 52
\n" ); document.write( "simplify to get:
\n" ); document.write( "3x^2 = 12
\n" ); document.write( "divide both sides by 3 to get:
\n" ); document.write( "x^2 = 4
\n" ); document.write( "solve for x to get x = plus or minus 2.\r
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\n" ); document.write( "\n" ); document.write( "those will be the x-coordinates of the intersection points.\r
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\n" ); document.write( "\n" ); document.write( "now we'll solve for y.\r
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\n" ); document.write( "\n" ); document.write( "in the first equation, replace x^2 with 4 to get:\r
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\n" ); document.write( "\n" ); document.write( "x^2 + y^2 = 52 becomes 4 + y^2 = 52
\n" ); document.write( "subtract 4 from both sides of this equation to get:
\n" ); document.write( "y^2 = 48
\n" ); document.write( "take the square root of both sides of this equation to get:
\n" ); document.write( "y = plus or minus sqrt(48) = 6.92820323.\r
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\n" ); document.write( "\n" ); document.write( "your x values are plus or minus 2.
\n" ); document.write( "your y values are plus or minus 6.92820323 which is equal to 6.928 rounded to 3 decimal places.\r
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\n" ); document.write( "\n" ); document.write( "your intersection points will be:
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document.write( "                       x           y\r\n" );
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document.write( "                      -2          -6.928\r\n" );
document.write( "                      -2           6.928\r\n" );
document.write( "                       2          -6.928\r\n" );
document.write( "                       2           6.928\r\n" );
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\n" ); document.write( "\n" ); document.write( "if you replace any of these point pair combinations in the original equations, those equations will be true.\r
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\n" ); document.write( "\n" ); document.write( "these same intersection points are shown on the graph.
\n" ); document.write( "the algebraic solution is equivalent to the graphical solution.\r
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