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Unformatted text preview: glance this might appear to be the same problem as the previous example. However, in
that case we ended up with an equality that simply wasn’t true. In this case we have 0=0 and that
is a true equality and so in that sense there is nothing wrong with this.
However, this is clearly not what we were expecting for an answer here and so we need to
determine just what is going on.
We’ll leave it to you to verify this, but if you find the slope and y-intercepts for these two lines
you will find that both lines have exactly the same slope and both lines have exactly the same yintercept. So, what does this mean for us? Well if two lines have the same slope and the same yintercept then the graphs of the two lines are the same graph. In other words, the graphs of these
two lines are the same graph. In these cases any set of points that satisfies one of the equations
will also satisfy the other equation.
Also, recall that the graph of an equation is nothing more than the set of all points that satisfies
the equation. In other words, there is an infinite set of points that will satisfy this set of equations.
In these cases we do want to write down something for a solution. So what we’ll do is solve one
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12