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