### 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.