### Video Transcript

Write down the set of simultaneous
equations that could be solved using the matrix equation. I’ve got two, negative one, two,
two, negative one, five, four, negative one, six multiplied by 𝑝, 𝑞, 𝑟, is equal
to four, 14, and 10.

When trying to work out which
simultaneous equations could be solved, we’re gonna start by looking at our first
matrix and looking at each column. Our first column represents the
𝑝-coefficients. Our second column represents our
𝑞-coefficients. And our third column represents our
𝑟-coefficients. So this is gonna be really useful
now when we’re actually looking to form our equations. And also if we look at our first
matrix, we can say that it’s a three-by-three matrix. And this helps tell us that there’s
gonna be three simultaneous equations that we need to find.

Now if we take a look at the answer
matrix, what this tells us, this actually tells us what values our simultaneous
equations are gonna be equal to. Okay, great! So we’ve now got all the
information we need. So let’s form our simultaneous
equations.

Our first term in our first
equation is going to be two 𝑝. And that’s because we’ve got a
coefficient of two here. And then that’s two 𝑝 because as
we said, the first column is all our coefficients of 𝑝. But also if you’re looking at
what’s happening, we actually multiply the term by 𝑝 in the second matrix.

Our second term in our first
equation is gonna be positive two 𝑞. And again, this is because we look
in our 𝑞 column and we see that the coefficient is two. And then finally, we’re gonna have
plus four 𝑟. And then from the answer matrix, we
can say that this is all gonna be equal to four. Okay, fantastic! We’ve got our first simultaneous
equation.

For our second equation, we’re
gonna start off with negative 𝑝. And be careful again with positives
and negatives. And this is if we’re looking, our
first matrix, we can see that it’s a negative one. So that’s why we’ve got negative
𝑝. And then we have minus 𝑞. And again, this is because I’ve got
negative one in our middle 𝑞 column and then finally minus 𝑟. And this is all gonna be equal to
14, which we again get from our answer matrix.

So, great! We’ve now got two simultaneous
equations. Now move on to the final one. We’re gonna have two 𝑝 plus five
𝑞 plus six 𝑟 is equal to 10. Okay, great! So we can now say that the set of
simultaneous equations that could be solved by a matrix equation are one, which is
two 𝑝 plus two 𝑞 plus four 𝑟 equals four; our second one, which is negative 𝑝
minus 𝑞 minus 𝑟 is equal to 14; and finally two 𝑝 plus five 𝑞 plus six 𝑟 equals
10.