document.write( "Question 30000: Find the real solutions, if any, of each system.\r
\n" ); document.write( "\n" ); document.write( "{4x^2 + 9y^2= 36}
\n" ); document.write( "{y= x+3}\r
\n" ); document.write( "\n" ); document.write( "I get stuck after setting everything to zero!
\n" ); document.write( "Thankyou \n" ); document.write( "

Algebra.Com's Answer #16757 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
[1] $\"4%2Ax%5E2+%2B+9%2Ay%5E2=+36\"$
\n" ); document.write( "[2] $\"y+=+x%2B3\"$
\n" ); document.write( "Substitute $\"y+=+x%2B3\"$ in [1]
\n" ); document.write( " $\"4%2Ax%5E2+%2B+9%2A%28x+%2B+3%29%5E2+=+36\"$
\n" ); document.write( " $\"4%2Ax%5E2+%2B+9%2A%28x%5E2+%2B+6%2Ax+%2B+9%29+=+36\"$
\n" ); document.write( " $\"4%2Ax%5E2+%2B+9%2Ax%5E2+%2B+54%2Ax+%2B+81+=+36\"$
\n" ); document.write( " $\"13%2Ax%5E2+%2B+54%2Ax+%2B+45+=+0\"$
\n" ); document.write( "use
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%28-54+%2B-+sqrt%28+54%5E2-4%2A13%2A45+%29%29%2F%282%2A13%29+\"$
\n" ); document.write( " $\"x+=+%28-54+%2B-+sqrt%28+2916-2340+%29%29%2F%2826%29\"$
\n" ); document.write( " $\"x+=+%28-54+%2B-+sqrt%28+576+%29%29%2F%2826%29\"$
\n" ); document.write( " $\"x+=+%28-54+%2B-+24%29%2F%2826%29\"$
\n" ); document.write( " $\"x+=+%28-27+%2B-+12%29%2F%2813%29\"$
\n" ); document.write( "[3] $\"x+=+-15%2F13\"$
\n" ); document.write( "[4] $\"x+=+-3\"$
\n" ); document.write( "substitute [3] in [2]
\n" ); document.write( " $\"y+=+-15%2F13+%2B+3\"$
\n" ); document.write( " $\"y+=+-15%2F13+%2B+39%2F13\"$
\n" ); document.write( " $\"y+=+24%2F13\"$
\n" ); document.write( "[5] (-15/13 , 24/13) is one solution
\n" ); document.write( "substitute [4] in [2]
\n" ); document.write( " $\"y+=+-3+%2B+3\"$
\n" ); document.write( " $\"y+=+0\"$
\n" ); document.write( "[6] (-3 , 0) is the other solution
\n" ); document.write( "check [5] in [1]
\n" ); document.write( " $\"4%2A%28-15%2F13%29%5E2+%2B+9%2A%2824%2F13%29%5E2=+36\"$
\n" ); document.write( " $\"4%2A%28-15%2F13%29%5E2+%2B+9%2A%2824%2F13%29%5E2=+36\"$
\n" ); document.write( "Multiply both sides by 13^2
\n" ); document.write( " $\"4%2A%28-15%29%5E2+%2B+9%2A%2824%29%5E2=+36+%2A+13%5E2\"$
\n" ); document.write( " $\"4+%2A+225+%2B+9+%2A+576+=+6084\"$
\n" ); document.write( " $\"900+%2B+5184+=+6084\"$
\n" ); document.write( " $\"6084+=+6084\"$
\n" ); document.write( "OK
\n" ); document.write( "check [6] in [1]
\n" ); document.write( " $\"4%2A%28-3%29%5E2+%2B+9%2A%280%29%5E2=+36\"$
\n" ); document.write( " $\"4+%2A+9+%2B+0+=+36\"$
\n" ); document.write( " $\"36+=+36\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );