### Video Transcript

By first multiplying the equations to make the coefficients of either π₯ or π¦
equal, use the elimination method to solve the given simultaneous equations to find π₯ and π¦:
two π₯ plus three π¦ equals four; three π₯ plus four π¦ equals eight.

The elimination method looks something like this. Itβs when your variable terms can cancel each other out if you add them together.
So in this example that I have drawn, two π₯ minus two π₯ would be zero and the π₯ term would
drop out. Now back to our problem, we actually donβt have any terms that are equal. Two π₯ and three π¦ canβt be added together; three π¦ and four π₯ cannot be added together. What we want to do is multiply both of these equations by numbers so that the coefficients of one of the variables, either π₯ or π¦, are equal in
both of these equations.

For example, if I multiplied the equation on the left by three, then I would
multiply three times two π₯, which would give me six π₯. I can then multiply the equation on the right by two; in this case weβd be multiplying two times three π₯, which would give us six π₯.

And now, we will have two equal variables that we could work with. So letβs go with three on the left side. Three times two π₯ equals six, three times three π¦ equals nine π¦, three times four equals 12.

And our equation on the right, weβll multiply by two. Two times three π₯ equals six π₯, two times four π¦ equals eight π¦, two times eight equals 16.

Now weβll take our first equation and subtract our second equation from the first. Here, weβll take six π₯ from six π₯, which would equal zero. After that, we need to subtract eight π¦ from nine π¦. So we say nine π¦
minus eight π¦ equals one π¦. And finally, 12 minus 16 equals negative four. This tells us that our π¦-value is negative four.

But what we want to do now is to use one of the equations and plug in negative four
for π¦. And our equation would look like this: two π₯ plus three times negative four
equals four. We multiply three times negative four to equal negative 12. Bring down our two π₯ and our four. To isolate π₯, weβll need to add 12 to both sides of our equation. On the left side, weβre left with two π₯. On the right side, four plus 12 equals 16.

Our final step to solve for π₯ would be to divide both sides of the equation by
two. Two π₯ divided by two equals π₯; 16 divided by two equals eight. This tells us that our π₯-value equals eight and our π¦-value equals negative four.