# Video: Expressing a Set of Simultaneous Equations as a Matrix Equation

Express the given set of simultaneous equations as a matrix equation. 3𝑥 = 12 + 5𝑦 + 2𝑧, 𝑥 − 5𝑦 = 21, 11𝑥 − 8𝑦 = −10 + 2𝑧.

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### Video Transcript

Express the given set of simultaneous equations as a matrix equation. Three 𝑥 equals 12 plus five 𝑦 plus two 𝑧, 𝑥 minus five 𝑦 equals 21, 11𝑥 minus eight 𝑦 equals negative 10 plus two 𝑧.

To solve this as a matrix equation, we need to get all of our variables lined up together. So let’s put each equation in the order of 𝑥, then 𝑦, then 𝑧 equals a constant. Our first equation would be three 𝑥 minus five 𝑦 minus two 𝑧 equals 12. Our next equation would be pretty much the same except there is no 𝑧 term. So we have 𝑥 minus five 𝑦 plus zero 𝑧 equals 21. And then our last equation will be 11𝑥 minus eight 𝑦 minus two 𝑧 equals negative 10.

To multiply matrices, we will take a row times a column. So we’ll have three times 𝑥, negative five times 𝑦, and negative two times 𝑧, would equal 12. That will be our first equation. Then we would have one times 𝑥, negative five times 𝑦, and zero times 𝑧, equals 21. That’s our second equation. And then 11 times 𝑥, negative eight times 𝑦, negative two times 𝑧, equals negative 10.

And this is how you would express these simultaneous equations as a matrix equation.