Question

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

3x + 2y + 25 = 0, 2x + y + 10 = 0

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

3x + 2y + 25 = 0, 2x + y + 10 = 0

Answer 1

The given equations are:

3x + 2y + 25 = 0   ...(i)

2x + y + 10 = 0   ...(ii)

Here a₁ = 3, b₁ = 2, c₁ = 25, a₂ = 2, b₂ = 1 and c₂ = 10

By cross multiplication, we have:

`∴ x/([2 xx 10 - 25 xx 1]) = y/([25 xx 2 - 10 xx 3]) = 1/([3 xx 1 - 2 xx 2])`

⇒ `x/((20 - 25)) = y/((50 - 30) ) = 1/((3 - 4))`

⇒ `x/((-5)) = y/20 = 1/((-1))`

⇒ `x = (-5)/(-1) = 5, y = 20/((-1)) = -20`

Hence, x = 5 and y = –20 is the required solution.