Questions: 7x - y = 6 3x + 2y = 22

7x - y = 6 3x + 2y = 22
Transcript text: $\begin{array}{l}7 x-y=6 \\ 3 x+2 y=22\end{array}$
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Solution

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Solution Steps

Step 1: Calculate the determinant

The determinant is calculated as $\Delta = a_1b_2 - a_2b_1 = 7 \times 2 - 3 \times -1 = 17.$

Step 2: Solve for x and y using Cramer's Rule

Using Cramer's Rule, $x = \frac{c_1b_2 - c_2b_1}{\Delta} = \frac{6 \times 2 - 22 \times -1}{17} = 2.$ Similarly, $y = \frac{a_1c_2 - a_2c_1}{\Delta} = \frac{7 \times 22 - 3 \times 6}{17} = 8.$

Final Answer:

The unique solution is $(x, y) = (2, 8).$

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