# Video: US-SAT03S3-Q04-176186876391

If π¦ is 3 times as large as π₯ and π¦ β π₯ = 8, what is the value of π¦?

03:55

### Video Transcript

If π¦ is three times as large as π₯ and π¦ minus π₯ equals eight, what is the value of π¦?

First, letβs take the phrase π¦ is three times as large as π₯ and turn it into an equation. π¦ is three times as large as π₯. We can represent that as π¦ equals three π₯. And now we have two equations π¦ equals three π₯ and π¦ minus π₯ equals eight. We want both of these equations to be true, so we can set them equal to each other.

Weβll take our second equation and get it into the format of π¦ equals something. To do that, weβll add π₯ to both sides. And our second equation will then say π¦ equals eight plus π₯. Weβre interested in the case when π¦ equals three π₯ and π¦ equals eight plus π₯ are both true. So, we set them equal to each other. Three π₯ equals eight plus π₯.

And now solving for π₯, we subtract π₯ from both sides. Three π₯ minus π₯ equals two. And π₯ minus π₯ cancels out. To get rid of two π₯, weβll divide both sides by two, which leaves us on the left with π₯. And eight divided by two equals four. These two statements are true when π₯ equals four. And we need to plug that π₯-value in to find our π¦ since our question has asked what the value of π¦ is.

π¦ equals three π₯, and π₯ equals four. Three times four is 12. Our π¦ equals 12. We can check our answer here by plugging in what we found for π₯ and π¦ into the equation π¦ minus π₯ equals eight. 12 minus four is equal to eight. And 12 is three times larger than four. π¦ equals 12.

Letβs consider a second way to solve this problem. Weβll still need our two equations. Notice how with our second equation the first time we solved for π¦. This time weβre going to solve our second equation for π₯. To solve for π₯, weβll need to subtract π¦ from both sides, which leaves us with negative π₯ equals eight minus π¦. To get rid of that negative in front of our π₯, weβll multiply the whole equation by negative one.

Negative one times negative π₯ equals π₯. Negative one times eight equals negative eight. Negative one times negative π¦ equals positive π¦. π₯ equals negative eight plus π¦. Or we can rewrite that to say π₯ equals π¦ minus eight. This time we know what π₯ equals. So, we take what we found for π₯ and we plug it into our equation one.

We know that π₯ equals π¦ minus eight. So, when we plug that back in, our new equation says π¦ equals three times π¦ minus eight. Distribute the three, and you get three π¦. Three times negative eight is negative 24. π¦ equals three π¦ minus 24. To solve for π¦, weβll subtract three π¦ from both sides. One π¦ minus three π¦ equals negative two π¦. And negative two π¦ equals negative 24. Now weβll divide both sides by negative two. π¦ equals 12. Negative 24 divided by negative two equals positive 12.