Write down the set of simultaneous
equations that could be solved using the given matrix equation. 11, negative three, nine, four
multiplied by 𝑥, 𝑦 is equal to eight, 13.
As with any problem of this type,
we can solve it using matrix multiplication. When multiplying matrices, we need
to multiply each row of the first matrix by each column of the second matrix. Multiplying 11 by 𝑥 gives us
11𝑥. Negative three multiplied by 𝑦 is
equal to negative three 𝑦. This will be equal to the element
in the top row of our constant matrix, in this case, eight. Our first equation is 11𝑥 minus
three 𝑦 is equal to eight.
We then repeat this process with
the second row of our two-by-two coefficient matrix. Multiplying nine by 𝑥 gives us
nine 𝑥. Four multiplied by 𝑦 is four
𝑦. Our second equation is therefore
nine 𝑥 plus four 𝑦 is equal to 13. We now have a pair of linear
simultaneous equations that could be solved using the elimination or substitution
methods. These would give us the values of
𝑥 and 𝑦 that solve the matrix equation.