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Question
Solve the system of equations by using the method of cross multiplication:
x + 2y + 1 = 0,
2x – 3y – 12 = 0.
Solution
The given equations are:
x + 2y + 1 = 0 …….(i)
2x – 3y – 12 = 0 …….(ii)
Here a1 = `1, b_1 = 2, c_1 = 1, a_2 = 2, b_2 = -3 and c_2 = -12`
By cross multiplication, we have:
∴ `x/([2 xx(-12)-1xx(-3)]) = y/([1xx2-1xx(-12)]) = 1/([1xx(-3)-2xx2])`
⇒`x/((-24+3))= y/((2+12)) = 1/((-3-4))`
⇒`x/((-21)) = y/((14)) = 1/((-7))`
⇒` x = (-21)/(-7)= 3, y = 14/(-7) = -2`
Hence, x = 3 and y = -2 is the required solution.
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