Interpretation of Vectors in Two Dimensions
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Multiply first equation by 2: \(10x - 4y = 22\). Add to second equation: \((10x - 4y) + (3x + 4y) = 22 + 5\) ⇒ \(13x = 27\) ⇒ x = \(\frac{27}{13}\). Substitute into second equation: \(3(\frac{27}{13}) + 4y = 5\) ⇒ \(\frac{81}{13} + 4y = 5\) ⇒ \(4y = 5 - \frac{81}{13} = \frac{65}{13} - \frac{81}{13} = -\frac{16}{13}\) ⇒ y = \(-\frac{4}{13}\).
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