### Video Transcript

Given that π₯ squared plus π₯π¦
equals 18 and π₯ plus π¦ equals six, find the value of π₯.

What we have here is a
linear-quadratic system of equations. The first equation π₯ plus π¦
equals six is linear. And the second equation π₯
squared plus π₯π¦ equals 18 is quadratic because it includes an π₯ squared term
and also the term π₯π¦, where the two variables are multiplied together. Weβre not asked to fully solve
this system of equations but simply to find the value of π₯. So weβre going to do this using
the substitution method.

We begin by rearranging the
first equation to give π¦ equals six minus π₯ because this gives an expression
for π¦ in terms of π₯, which we can substitute into the second equation to give
an equation in π₯ only. Doing so gives the equation π₯
squared plus π₯ multiplied by six minus π₯ equals 18. And we now have a quadratic
equation in π₯, which we can solve.

We distribute the parentheses
on the left-hand side to give π₯ squared plus six π₯ minus π₯ squared equals
18. And we now see that the π₯
squared and negative π₯ squared terms will cancel each other out. So, in fact, our equation
reduces to a linear equation. We have six π₯ is equal to
18. And this equation can be solved
by dividing each side by six to give π₯ equals three. So by substituting π¦ equals
six minus π₯ into the second equation, we created an equation in π₯ only which
we could then solve to find the value of π₯.

Of course, we arenβt asked to
find the value of π¦ in this problem. But if we did need to, we could
substitute the value of π₯ weβve just found back into our linear equation, π¦
equals six minus π₯, to find the corresponding value of π¦. Our solution to the problem is
that the value of π₯ is three.