Questions: 2x-3y=3 -2x+y=-4

Transcript text: 2x-3y=3 -2x+y=-4

Solution

Solution Steps

Step 1: Calculate the determinant

The determinant is calculated as $\Delta = a_1b_2 - a_2b_1 = 2 \times 1 + 2 \times -3 = -4.$

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

Using Cramer's Rule, $x = \frac{c_1b_2 - c_2b_1}{\Delta} = \frac{3 \times 1 + 4 \times -3}{-4} = 2.25.$ Similarly, $y = \frac{a_1c_2 - a_2c_1}{\Delta} = \frac{2 \times -4 + 2 \times 3}{-4} = 0.5.$

Final Answer:

The unique solution is $(x, y) = (2.25, 0.5).$

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