document.write( "Question 1005383: How would you solve the quadratic linear system algebraically which is y=4x^2-6x-10 and y=25-2x? \n" ); document.write( "

Algebra.Com's Answer #621672 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( " $\"y=4x%5E2-6x-10\"$
\n" ); document.write( " $\"y=25-2x\"$
\n" ); document.write( "Since both equal y:
\n" ); document.write( " $\"4x%5E2-6x-10=25-2x\"$
\n" ); document.write( " $\"4x%5E2-4x-35=0\"$
\n" ); document.write( " $\"%284x%2B10%29%28x-3.5%29=0\"$
\n" ); document.write( " $\"4x%2B10=0\"$ $\"OR\"$ $\"x-3.5=0\"$
\n" ); document.write( " $\"4x=-10\"$ $\"OR\"$ $\"x=3.5\"$
\n" ); document.write( " $\"x=-2.5\"$ $\"OR\"$ $\"x=3.5\"$
\n" ); document.write( ".
\n" ); document.write( "Using x=(-2.5):
\n" ); document.write( " $\"y=25-2x\"$
\n" ); document.write( " $\"y=25-2%28-2.5%29\"$
\n" ); document.write( " $\"y=25-%28-5%29\"$
\n" ); document.write( " $\"y=30\"$
\n" ); document.write( ".
\n" ); document.write( "CHECK (Using other equation):
\n" ); document.write( " $\"y=4x%5E2-6x-10\"$
\n" ); document.write( " $\"30=4%28-2.5%29%5E2-6%28-2.5%29-10\"$
\n" ); document.write( " $\"30=4%286.25%29-%28-15%29-10\"$
\n" ); document.write( " $\"30=25%2B15-10\"$
\n" ); document.write( " $\"30=40-10\"$
\n" ); document.write( " $\"30=30\"$
\n" ); document.write( ".
\n" ); document.write( "Using x=3.5:
\n" ); document.write( " $\"y=25-2x\"$
\n" ); document.write( " $\"y=25-2%283.5%29\"$
\n" ); document.write( " $\"y=25-7\"$
\n" ); document.write( " $\"y=18\"$
\n" ); document.write( ".
\n" ); document.write( "CHECK:
\n" ); document.write( " $\"y=4x%5E2-6x-10\"$
\n" ); document.write( " $\"18=4%283.5%29%5E2-6%283.5%29-10\"$
\n" ); document.write( " $\"18=4%2812.25%29-21-10\"$
\n" ); document.write( " $\"18=49-31\"$
\n" ); document.write( " $\"18=18\"$
\n" ); document.write( ".
\n" ); document.write( "ANSWER: The solutions are (-2.5,30) and (3.5,18) \n" ); document.write( "

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