document.write( "Question 29299: I need help with solving the system of equations algebraically. The problem is : y=2x^2
\n" ); document.write( " y= x+3 \n" ); document.write( "

Algebra.Com's Answer #16095 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Try this:
\n" ); document.write( " $\"y+=+2x%5E2\"$ and $\"y+=+x%2B3\"$ Since y = y you can write:
\n" ); document.write( " $\"2x%5E2+=+x%2B3\"$ Simplify.
\n" ); document.write( " $\"2x%5E2-x-3+=+0\"$ Solve this quadratic by factoring.
\n" ); document.write( " $\"%282x-3%29%28x%2B1%29+=+0\"$ Apply the zero products principle.
\n" ); document.write( " $\"2x-3+=+0\"$ and/or $\"x%2B1+=+0\"$
\n" ); document.write( "If $\"2x-3+=+0\"$ then $\"2x+=+3\"$ and $\"x+=+3%2F2\"$
\n" ); document.write( "If $\"x%2B1+=+0\"$ then $\"x+=+-1\"$ \r
\n" ); document.write( "\n" ); document.write( "We have found the x-coordinates of the solutions. To find the y-coordinates, substitute the x-values into either of the original equations and solve for y.\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+3%2F2\"$ Substitute into $\"y+=+x%2B3\"$
\n" ); document.write( " $\"y+=+3%2F2+%2B+3\"$
\n" ); document.write( " $\"y+=+3%2F2+%2B+6%2F2\"$
\n" ); document.write( " $\"y+=+9%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-1\"$ Substitute into $\"y+=+2x%5E2\"$
\n" ); document.write( " $\"y+=+2%28-1%29%5E2\"$
\n" ); document.write( " $\"y+=+2\"$ \r
\n" ); document.write( "\n" ); document.write( "The solutions are:
\n" ); document.write( "(3/2, 9/2) and (-1, 2)\r
\n" ); document.write( "\n" ); document.write( "Why are there two solutions? Because you have a parabola $\"y+=+2x%5E2\"$ transversed by a line $\"y+=+x%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( "Here's a graph showing the two intersections/solutions.
\n" ); document.write( " $\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C2x%5E2%2Cx%2B3%29\"$ \n" ); document.write( "

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