# Worked example: solutions to 2-variable equations

## Video transcript

- [Voiceover] "Which of
the ordered pairs is a "solution of the following equation?" 4x minus one is equal to 3y plus five. Now, when we look at an
ordered pair we wanna figure out whether it's a
solution, we just have to remind ourselves that
in these ordered pairs the convention, the standard,
is is that the first coordinate is the x coordinate,
and the second coordinate is the y coordinate. So they're gonna, if this is
a solution, if this ordered pair is a solution, that means
that if x is equal to three and y is equal to two,
that that would satisfy this equation up here. So let's try that out. So, we have four times x. Well we're saying x needs
to be equal to three, minus one, is going to be
equal to three times y. Well, if this ordered
pair is a solution then y is going to be equal
to two, so three times y, y is two, plus five. Notice all I did is wherever I saw the x, I substituted it with three, wherever I saw the y, I
substituted it with two. Now let's see if this is true. Four times three is twelve, minus one. Is this really the same
thing as three times two which is six, plus five? See, 12 minus one is 11, six plus five is also 11. This is true, 11 equals 11. This pair three, two does
satisfy this equation. Now let's see whether
this one does, two, three. So this is saying when x is equal to two, y would be equal to
three for this equation. Let's see if that's true. So four times x, we're
now gonna see if when x is two, y can be three. So four times x, four times two, minus one is equal to three times y, now y we're testing to
see if it can be three. Three times three plus five, let's see if this is true. Four times two is eight, minus one, is this equal to three times three? So that's nine plus five. So is seven equal to 14? No, clearly seven is not equal to 14. So these things are not
equal to each other. So this is not a solution,
when x equals two y cannot be to three and
satisfy this equation. So only three, two is a solution.