![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
They will have the same solution at the points where the graphs of each equation intersect each other.
\n" ); document.write( "An example would be:
\n" ); document.write( "x^2 + 5x + 3
\n" ); document.write( "-x^2 + 5x + 6
\n" ); document.write( "The graph of both of these equations is shown below:
\n" ); document.write( "
\n" ); document.write( "The graph of these equations show that they will intersect at 2 places.
\n" ); document.write( "Those places would be the common solutions for both equations.
\n" ); document.write( "To find the intersection points, set the equations equal to each other and solve.
\n" ); document.write( "We start with:
\n" ); document.write( "x^2 + 5x + 3 = -x^2 + 5x + 6
\n" ); document.write( "Add x^2 to both sides of this equation and subtract 5x from both sides of this equation and subtract 6 from both sides of this equation to get:
\n" ); document.write( "2x^2 - 3 = 0
\n" ); document.write( "Add 3 to both sides of this equation to get:
\n" ); document.write( "2x^2 = 3
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "x^2 = 3/2
\n" ); document.write( "Take the square root of both sides of this equation to get:
\n" ); document.write( "x = +/- sqrt(3/2)
\n" ); document.write( "The 2 equations should intersect at the same value of y when x = +/- sqrt(3/2).
\n" ); document.write( "That would be a common solution for both graphs.
\n" ); document.write( "Our 2 equations are:
\n" ); document.write( "y1 = x^2 + 5x + 3
\n" ); document.write( "y2 = -x^2 + 5x + 6
\n" ); document.write( "When x = + sqrt(3/2), these equations become:
\n" ); document.write( "y1 = 10.62372436
\n" ); document.write( "y2 = 10.62372436
\n" ); document.write( "x = + sqrt(3/2) is roughly located at x = 1.2
\n" ); document.write( "Look at the graph and you'll see that when x = 1.2, the 2 equations intersect at somewhere around y = 10.6.
\n" ); document.write( "When x = - sqrt(3/2), these equations become:
\n" ); document.write( "y1 = -1.623624357
\n" ); document.write( "y2 = -1.623724357
\n" ); document.write( "x = - sqrt(3/2) is roughly located at x = -1.2
\n" ); document.write( "Look at the graph and you'll see that when x = -1.2, the 2 equations intersect at somewhere around y = -1.6.
\n" ); document.write( "If you want to see what the graph of those equations looks like from a more distant perspective, it is shown below:
\n" ); document.write( "