Question

Solve the system of equations by using the method of cross multiplication:
3x - 2y + 3 = 0,
4x + 3y – 47 = 0

Answer 1

The given equations are:

3x - 2y + 3 = 0 …….(i)
4x + 3y – 47 = 0 …….(ii)
Here` a_1 = 3, b_1 = -2, c_1 = 3, a_2 = 4, b_2 = 3 and c_2 = -47`
By cross multiplication, we have:

∴ `x/([(−2)×(−47)−3 × 3]) = y/[(3 ×4 −(−47)× 3]) = 1/([3 ×3 −(−2) × 4])`

`⇒x/((94−9)) = y/((12+141) )= 1/((9+8))`

`⇒x/((85)) = y/((153)) = 1/((17))`

`⇒x = 85/17 = 5, y = 153/17 = 9`
Hence, x = 5 and y = 9 is the required solution.