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Question
Solve the system of equations by using the method of cross multiplication:
7x - 2y – 3 = 0,
`11x - 3/2 y – 8 = 0.`
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Solution
The given equations may be written as:
7x - 2y – 3 = 0 …….(i)
`11x - 3/2 y – 8 = 0` …….(ii)
Here a1 = 7, b1 = -2, c1 = -3, a2 = 11, b2 = - `3/2` and c2 = -8
By cross multiplication, we have:
`∴ x/([(−2)×(−8) −(−32) ×(−3)]) = y/([(−3) × 11 −(−8) × 7])= 1/[(7 × (−32)−11 ×(−2)])`
`⇒x/((16− 9/2)) = y/((−33+56)) = 1/((−21/2 + 22))`
`⇒x/((23/2)) = y/23 = 1/((23/2))`
`⇒x = (23/2)/(23/2) = 1, y = 23/(23/2) = 2`
Hence, x = 1 and y = 2 is the required solution.
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