Question

Solve the system of equations by using the method of cross multiplication:

x + 2y + 1 = 0, 2x – 3y – 12 = 0

Solve the following system of equations by using the method of cross multiplication:

x + 2y + 1 = 0, 2x – 3y – 12 = 0

Answer 1

The given equations are:

x + 2y + 1 = 0   ...(i)

2x – 3y – 12 = 0   ...(ii)

Here a₁ = 1, b₁ = 2, c₁ = 1, a₂ = 2, b₂ = –3 and c₂ = –12

By cross multiplication, we have:

∴ `x/([2 xx (-12) - 1 xx (-3)]) =  y/([1 xx 2 - 1 xx (-12)]) = 1/([1 xx (-3) -2 xx 2])`

⇒ `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.