Question Video: Identifying a Pair of Simultaneous Equations from a Matrix Equation Mathematics

Write down the set of simultaneous equations that could be solved using the given matrix equation. [11, −3 and 9, 4][𝑥 and 𝑦] = [8 and 13]

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Video Transcript

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.

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