Video Transcript
If 𝑥, 𝑦 is the solution of the
system of equations 𝑥 over 𝑦 equals seven, three multiplied by 𝑦 plus four equals
𝑥, what is the value of 𝑥?
Well, in this question the first
thing I’m going to do is I’m gonna label the equations because we got a pair of
equations here, which can also be known as simultaneous equations. So we’ve got equation one and
equation two.
So the first thing we’re going to
do is I’m going to rearrange equation one. And what I’m going to do is
rearrange it to make 𝑥 the subject of the equation. And to make 𝑥 the subject of the
equation, what I’m gonna do is multiply each side of the equation by 𝑦. And when I do that, what’s gonna
happen is we’re gonna have 𝑥 over 𝑦 multiplied by 𝑦 which would just give us 𝑥
and seven multiplied by 𝑦 which will give us seven 𝑦. So we have 𝑥 is equal to seven
𝑦. And I’m going to call this equation
three.
Now, this method is called
substitution because what we’re going to do is substitute equation three into
equation two. So what this means is we’re gonna
swap any 𝑥-value in equation two for seven 𝑦. And when I do that, I get three
multiplied by 𝑦 plus four is equal to seven 𝑦. And that’s because I’ve now
exchanged the 𝑥 for seven 𝑦.
Okay, great, what’s the next
step? Well, the next step is to
distribute three over the terms in the parenthesis. So to do that, the first thing I’m
gonna do is multiply three by 𝑦. And that’s gonna give us three
𝑦. And then, I’m gonna multiply three
by four or positive four which is gonna give us positive 12. So we now have three 𝑦 plus 12
equals seven 𝑦.
So now, what we’re going to do is
solve to find 𝑦. And to do that, what we’re going to
do is subtract three 𝑦 from each side of the equation. And when we do that, we’re gonna
get 12 is equal to four 𝑦. And that’s because three 𝑦 minus
𝑦 is zero and seven 𝑦 minus three 𝑦 is four 𝑦.
So now, the next stage is to divide
each side of the equation by four because we want single 𝑦. And when we divide each side of the
equation by four, we’re gonna get three is equal to 𝑦. So we’ve now found our
𝑦-value. However, the question isn’t looking
for us to find the value of 𝑦; it wants us to find the value of 𝑥. So how are we gonna use this to
find 𝑥?
Well to find 𝑥, what we’re going
to do is substitute 𝑦 equals three into equation three because that’s gonna allows
to find out what our 𝑥-value is. So when we do that, we get 𝑥 is
equal to seven multiplied by three which is gonna give us a value of 𝑥 is equal to
21. So we now solved the problem.
But what I’m gonna do is I’m gonna
check that this is the correct answer by substituting 𝑥 equals 21 into equation
two. And as well as 𝑥 equals 21, I’m
also gonna substitute in 𝑦 equals three cause that’s gonna let me see if they are
both the correct values. So when I do that, I get three
multiplied by three plus four is equal to 21. Well, three multiplied by three
plus four is three multiplied by seven. So yes, this will give us 21.
So we can say that 𝑥 is 21 is the
correct solution to the value of 𝑥 in our system of equations.
