2X + 3Y = [8, -1; -3, 6] and 3X + 2Y = [7, -4; -2, 9]. What is X?

Question 43

HardOriginal question

$2X + 3Y = \begin{bmatrix}8 & -1 \\ -3 & 6\end{bmatrix}$ and $3X + 2Y = \begin{bmatrix}7 & -4 \\ -2 & 9\end{bmatrix}$ . What is $X$ ?

\begin{bmatrix}1 & -2 \\ 0 & 3\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}-1 & 2 \\ 0 & -3\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}2 & 1 \\ -1 & 0\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}3 & -1 \\ -1 & 3\end{bmatrix}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Remove $Y$ : three times the second equation minus twice the first gives $9X - 4X = 5X$ .
$5X = 3\begin{bmatrix}7 & -4 \\ -2 & 9\end{bmatrix} - 2\begin{bmatrix}8 & -1 \\ -3 & 6\end{bmatrix} = \begin{bmatrix}5 & -10 \\ 0 & 15\end{bmatrix}$ .
So $X = \begin{bmatrix}1 & -2 \\ 0 & 3\end{bmatrix}$ .

Worth noting

$\begin{bmatrix}-1 & 2 \\ 0 & -3\end{bmatrix}$ comes from subtracting the other way, $2P - 3Q = -5X$ , and forgetting the minus sign.

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