Question

Solve the system of equations by using the method of cross multiplication:
2x + y – 35 = 0,
3x + 4y – 65 = 0

Answer 1

The given equations may be written as:
2x + y – 35 = 0                          …….(i)

3x + 4y – 65 = 0 …….(ii)
Here a1 = 2, b1 = 1, c1 = -35, a2 = 3, b2 = 4 and c2 = -65
By cross multiplication, we have:

`∴ x/((1×(−65) −4 ×(−35)]) = Y/([(−35) × 3 −(−65) × 2]) = 1/([2 × 4−3 × 1])`

`⇒x/((−65+140) )= y/((−105+130) )= 1/((8−3))`

`⇒x/75 = y/25 = 1/5`

`⇒ x = 75/5 = 15, y = 25/5 = 5`
Hence, x = 15 and y = 5 is the required solution.