SOLUTION: explain how you can deteremine whether a pair of linear equations has a unique solution.

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Question 249503: explain how you can deteremine whether a pair of linear equations has a unique solution.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
if the determinant is zero there is one solution.
b^2-4ac is the determinant from the quadratic formula.
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:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A2=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%284%29%29%2F2%5C2.
Expression can be factored: 2x%5E2%2B4x%2B2+=+2%28x--1%29%2A%28x--1%29

Again, the answer is: -1, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B2+%29