document.write( "Question 249503: explain how you can deteremine whether a pair of linear equations has a unique solution. \n" ); document.write( "

Algebra.Com's Answer #186369 by richwmiller(17219) $\"\"$ $\"About$

You can put this solution on YOUR website!
if the determinant is zero there is one solution.
\n" ); document.write( "b^2-4ac is the determinant from the quadratic formula.
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"2x%5E2%2B4x%2B2+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%284%29%5E2-4%2A2%2A2=0\"$ .
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\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: $\"x+=+%28-%284%29%29%2F2%5C2\"$ .
\n" ); document.write( " Expression can be factored: $\"2x%5E2%2B4x%2B2+=+2%28x--1%29%2A%28x--1%29\"$
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\n" ); document.write( " Again, the answer is: -1, -1.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B2+%29\"$

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