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## Analyzing the number of solutions to linear equations

Current time:0:00Total duration:1:23

## Video transcript

We're asked to use
the drop-downs to form a linear equation
with no solutions. So a linear equation
with no solutions is going to be one where I don't
care how you manipulate it, the thing on the
left can never be equal to the thing on the right. And so let's see what
options they give us. One, they want us to-- we
can pick the coefficient on the x term and then
we can pick the constant. So if we made this
negative 11x, so now we have a negative
11x on both sides. Here on the left hand side,
we have negative 11x plus 4. If we do something other
than 4 here, so if we did say negative 11x minus
11, then here we're not going to have any solutions. And you say, hey, Sal how
did you come up with that? Well think about
it right over here. We have a negative 11x here,
we have a negative 11x there. If you wanted to solve
it algebraically you could add 11x to both sides
and both of these terms will cancel out with each other
and all you would be left with is a 4 is equal to
a negative 11, which is not possible for
any x that you pick. Another way that you
think about it is here we have negative 11
times some number and we're adding 4
to it, and here we're taking negative 11 times
that same number and we're subtracting 11 from it. So if you take a negative
11 times some number and on one side you add four,
and on the other side you subtract 11, there's no way, it
doesn't matter what x you pick. There's no x for which
that is going to be true. But let's check our
answer right over here.