document.write( "Question 206575: URGENT QUESTION NEEDED BY TOMORROW. hey there.. thankyou soom much..:) great help. the question is
\n" ); document.write( "solve.
\n" ); document.write( "2x-3y+1=0
\n" ); document.write( "x^2 -y^2=7
\n" ); document.write( "thank you so much \n" ); document.write( "
Algebra.Com's Answer #156120 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
2x-3y+1=0 (equation 1)
\n" ); document.write( "x^2 -y^2=7 (equation 2)
\n" ); document.write( ".
\n" ); document.write( "Solve equation 1 for y:
\n" ); document.write( "2x-3y+1=0
\n" ); document.write( "2x-3y=-1
\n" ); document.write( "-3y=-1-2x
\n" ); document.write( "3y=1+2x
\n" ); document.write( "y = 1/3 + (2x/3)
\n" ); document.write( ".
\n" ); document.write( "Plug the above into equation 2 and solve for x:
\n" ); document.write( "x^2 -y^2=7
\n" ); document.write( "x^2 -(1/3 + (2x/3))^2=7
\n" ); document.write( "x^2 -(1/3 + (2x/3))(1/3 + (2x/3))=7
\n" ); document.write( "x^2 -(1/9 + 2x/9 + 2x/9 + 4x^2/9 )=7
\n" ); document.write( "x^2 -(1/9 + 4x/9 + 4x^2/9 )=7
\n" ); document.write( "x^2 - 1/9 - 4x/9 - 4x^2/9 =7
\n" ); document.write( "9x^2 - 1 - 4x - 4x^2 = 63
\n" ); document.write( "5x^2 - 8x - 1 = 63
\n" ); document.write( "5x^2 - 8x - 64 = 0
\n" ); document.write( "Solving for x using the quadratic equation (see below) gives us:
\n" ); document.write( "x = {4.466, -2.866}
\n" ); document.write( ".
\n" ); document.write( "Plug back into equation 1 to find y:
\n" ); document.write( "When x =4.466
\n" ); document.write( "2x-3y+1=0
\n" ); document.write( "y = 1/3 + (2x/3)
\n" ); document.write( "y = 1/3 + (2(4.466)/3)
\n" ); document.write( "y = 1/3 + (8.932/3)
\n" ); document.write( "y = 1/3 + (8.932/3)
\n" ); document.write( "y = 3.311
\n" ); document.write( ".
\n" ); document.write( "When x =-2.866
\n" ); document.write( "2x-3y+1=0
\n" ); document.write( "y = 1/3 + (2x/3)
\n" ); document.write( "y = 1/3 + (2(-2.866)/3)
\n" ); document.write( "y = 1/3 + (-5.732/3)
\n" ); document.write( "y = 1/3 + (-1.911)
\n" ); document.write( "y = -1.577
\n" ); document.write( ".
\n" ); document.write( "Our two solutions are then:
\n" ); document.write( "(x,y) = (4.466, 3.311)
\n" ); document.write( "(x,y) = (-2.866, -1.577)
\n" ); document.write( ".
\n" ); document.write( "Details of quadratic to follow:
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"5x%5E2%2B-8x%2B-64+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-8%29%5E2-4%2A5%2A-64=1344\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=1344 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--8%2B-sqrt%28+1344+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+1344+%29%29%2F2%5C5+=+4.46606055596467\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-8%29-sqrt%28+1344+%29%29%2F2%5C5+=+-2.86606055596467\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"5x%5E2%2B-8x%2B-64\" can be factored:
\n" ); document.write( " \"5x%5E2%2B-8x%2B-64+=+5%28x-4.46606055596467%29%2A%28x--2.86606055596467%29\"
\n" ); document.write( " Again, the answer is: 4.46606055596467, -2.86606055596467.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-8%2Ax%2B-64+%29\"
\n" ); document.write( " \n" ); document.write( "
\n" );