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Question
Solve the system of equations by using the method of cross multiplication:
6x - 5y - 16 = 0,
7x - 13y + 10 = 0
Solution
The given equations are:
6x - 5y - 16 = 0 …….(i)
7x - 13y + 10 = 0 …….(ii)
Here `a_1 = 6, b_1 = -5, c_1 = -16, a_2 = 7, b_2 = -13 and c_2 = 10`
By cross multiplication, we have:
∴ `x/([(−5)×10 −(−16) ×(−13)]) = y/([(−16)×7 −10 × 6]) = 1/([6 ×(−13)−(−5) × 7])`
`⇒x/((−50−208)) = y/((−112−60)) = 1/((−78+35))`
`⇒x/(−258) = y/((−172)) = 1/((43))`
`⇒x = (−258)/(−43) = 6, y = (−172)/(−43) = 4`
Hence, x = 6 and y = 4 is the required solution.
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