### Video Transcript

If π¨ equals four π’ plus π£, π©
equals π minus two times π’ plus two π£, and π¨ is parallel to π©, then π equals
what.

Here we have these two
two-dimensional vectors π¨ and π©, and weβre told that theyβre parallel to one
another. Knowing this, we can recall that,
in general, whenever we have two vectors, say we call them π one and π two, that
are parallel, this means there exists some nonzero constant πΆ by which we can
multiply π two so it equals π one. Another mathematically equivalent
way of saying this is to write that the ratio of the π₯-component of π one to π
two equals the π¦-component of π one to π two.

And we can apply this relationship
to our two given vectors π¨ and π©. Because π¨ and π© are parallel, we
can say that π΄ sub π₯ over π΅ sub π₯ equals π΄ sub π¦ over π΅ sub π¦. We see that π΄ sub π₯ equals four,
π΅ sub π₯ equals π minus two, while π΄ sub π¦ equals one and π΅ sub π¦ is two. We now have an equation where
everything in it is known except for the unknown π.

If we multiply both sides of this
equation by π minus two and multiply both sides by two, we find the result that
four times two equals one times the quantity π minus two or eight equals π minus
two. Adding two to both sides, we find
that π equals 10. Thatβs our answer. So we can say that if π¨ equals
four π’ plus π£, π© equals π minus two π’ plus two π£, and π¨ is parallel to π©,
then π equals 10.