### Video Transcript

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

Weβve been given specific
instructions on the method to use to solve these simultaneous equations. We want to use the elimination
method. In the elimination method, you
either add or subtract to the equations to get an equation in one variable. This method works when the
coefficients of one of the variables are equal to each other.

Because none of our coefficients
are equal to each other, weβll first multiply the equations by some value to make
either the π₯ or π¦ equal: equation one two π₯ plus three π¦ equals four, and
equation two is three π₯ plus four π¦ equals eight. The π₯-terms have coefficients of
two and three, and the π¦-terms have coefficients three and four.

We could multiply through by many
different values. But itβs simplest to look for the
least common multiple. For example, with two and three as
the π₯-coefficients, the least common multiple would be six. And to have a coefficient of six,
we multiply the first equation through by three. This gives an equivalent equation:
six π₯ plus nine π¦ equals 12. For our second equation, we
multiply through by two, which produces six π₯ plus eight π¦ equals 16.

Using the elimination method, we
can subtract the second equation from the first equation, being careful to remember
that we are subtracting every term. So it might be helpful to
distribute that subtraction across the equation. Six π₯ minus six π₯ equals zero,
nine π¦ minus eight π¦ equals one π¦, and 12 minus 16 equals negative four.

Now that we found that π¦ equals
negative four, we can plug π¦ back into our first equation, our second equation, or
even these equivalent equations to solve for π₯. Using our first equation, two π₯
plus three π¦ equals four, if we plug in negative four for π¦, we see two π₯ minus
12 equals four. Adding 12 to both sides gives us
two π₯ equals 16. And dividing both sides by two, we
find that π₯ equals eight. The solution to this system of
equations is π₯ equals eight and π¦ equals negative four.