Question

Solve the 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 `a_1 = 3, b_1 = 2, c_1 = 25, a_2 = 2, b_2 = 1 and c_2 = 10`
By cross multiplication, we have:

\

`∴ x/([2×10 −25 × 1]) = y/([25 × 2 −10 × 3] )= 1/([3 × 1−2 × 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.