### 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.