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Mathematics

Solve, using cross-multiplication :

4x + 6y = 15

3x - 4y = 7

Linear Equations

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Answer

Given, equations

⇒ 4x + 6y = 15 and 3x - 4y = 7

⇒ 4x + 6y - 15 = 0 ……….(1)

⇒ 3x - 4y - 7 = 0 ………..(2)

By cross-multiplication we have :

⇒x6×(−7)−(−4)×(−15)=y(−15)×3−(−7)×4=14×(−4)−3×6⇒x−42−60=y−45+28=1−16−18⇒x−102=y−17=1−34⇒x−102=1−34 and y−17=1−34⇒x=−102−34 and y=−17−34⇒x=3 and y=12.\Rightarrow \dfrac{x}{6 \times (-7) - (-4) \times (-15)} = \dfrac{y}{(-15) \times 3 - (-7) \times 4} = \dfrac{1}{4 \times (-4) - 3 \times 6} \\[1em] \Rightarrow \dfrac{x}{-42 - 60} = \dfrac{y}{-45 + 28} = \dfrac{1}{-16 - 18} \\[1em] \Rightarrow \dfrac{x}{-102} = \dfrac{y}{-17} = \dfrac{1}{-34} \\[1em] \Rightarrow \dfrac{x}{-102} = \dfrac{1}{-34} \text{ and } \dfrac{y}{-17} = \dfrac{1}{-34} \\[1em] \Rightarrow x= \dfrac{-102}{-34} \text{ and } y = \dfrac{-17}{-34} \\[1em] \Rightarrow x = 3 \text{ and } y = \dfrac{1}{2}.

Hence, x = 3 and y = 12\dfrac{1}{2}.

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