document.write( "Question 62716: really need help
\n" ); document.write( "solve the system of nonlinear equations for x and y. sketch a graph of each equation showing the intersection points of the line and the parabola. x^2 + y=4 and 2x + y=1 thanks so much \n" ); document.write( "
Algebra.Com's Answer #43567 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
really need help
\n" ); document.write( "solve the system of nonlinear equations for x and y. sketch a graph of each equation showing the intersection points of the line and the parabola.\r
\n" ); document.write( "\n" ); document.write( " x^2 + y = 4 and 2x + y = 1
\n" ); document.write( "Solve it like any system, using the elimination method
\n" ); document.write( "x^2 + y = 4
\n" ); document.write( "2x + y = 1
\n" ); document.write( "------------ subtract
\n" ); document.write( "x^2 - 2x + 0y = 3; y is eliminated so you have:
\n" ); document.write( "x^2 - 2x - 3 = 0
\n" ); document.write( "Factor this to:
\n" ); document.write( "(x-3)(x+1) = 0
\n" ); document.write( "x = +3 and x = -1, the solution to this system
\n" ); document.write( ":
\n" ); document.write( "To graph this (you know the intersection points will be x=+3 and x=-1 from the above solution)
\n" ); document.write( ":
\n" ); document.write( "First arrange the equations in the general form (y=)
\n" ); document.write( "x^2 + y = 4
\n" ); document.write( "y = 4 - x^2
\n" ); document.write( ":
\n" ); document.write( "2x + y = 1
\n" ); document.write( "y = 1 - 2x
\n" ); document.write( ":
\n" ); document.write( "Write up a table to plot, y = 4 - x^2
\n" ); document.write( "Start with x = -5: ie y = 4 - (-5^2) = - 21
\n" ); document.write( ":
\n" ); document.write( "x | y
\n" ); document.write( "-----
\n" ); document.write( "-5|-21
\n" ); document.write( "-4|-12
\n" ); document.write( "-3|-5
\n" ); document.write( "-2|0
\n" ); document.write( "-1|+3; point of intersection
\n" ); document.write( "0 |+4
\n" ); document.write( "+2|0
\n" ); document.write( "+3|-5; point of intersection
\n" ); document.write( "+4|-12
\n" ); document.write( ":
\n" ); document.write( "Do the same with y = 1 - 2x, it's a straight line so a couple plots will do it
\n" ); document.write( "x | y
\n" ); document.write( "-----
\n" ); document.write( "-3|+7
\n" ); document.write( "-1|+3; point of intersection
\n" ); document.write( "0 |+1
\n" ); document.write( "+1|-1
\n" ); document.write( "+3|-5; point of intersection
\n" ); document.write( "+4|-7
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Your graph should look this
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+6%2C+-8%2C+8%2C+4-x%5E2%2C+1-2x%29+\"
\n" ); document.write( ":
\n" ); document.write( "Do you see the relationship between our solutions and the graph intersections?
\n" ); document.write( "you can email me if you have a question on this?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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