Question

Solve the system of equations by using the method of cross multiplication:
2x + 5y – 1 = 0, 2x + 3y – 3 = 0

Answer 1

The given equations may be written as:
2x + 5y – 1 = 0 …….(i)
2x + 3y – 3 = 0 …….(ii)
Here a1 = 2, b1 = 5, c1 = -1, a2 = 2, b2 = 3 and c2 = -3
By cross multiplication, we have:

`∴ x/([5×(−3) −3 ×(−1)] )= y/([(−1) × 2 −(−3) × 2]) = 1/([2 × 3−2 × 5])`

`⇒x/((−15+3))= y/((−2+6) )= 1/((6−10))`

`⇒x/(−12) = y/4 = 1/(−4)`

`⇒x = (−12)/(−4 )= 3, y = 4/(−4 )= -1`
Hence, x = 3 and y = -1 is the required solution.