Question

Solve using cross multiplication method:-

8x+5y=9

3x+2y=4

Answer 1

Solution:
As per cross multiplication method,

x/(b1c2−b2c1) =y/(c1a2−a2c1)= 1(a1b2−b2a1)

Here,
a1 and a2 are coefficients of variable x.

b1 and b2 are coefficients of variable y.

c1 and c2 are constant terms.

or, 8x + 5y - 9 = 0 ......i)
or, 3x + 2y - 4 = 0 .....ii)

Here, a1=8 and a2=3
b1=5 and b2=2
c1=-9 and c2=-4

We have:
x y 1
b1 c1 a1 b1
b2 c2 a2 b2

Putting all the values:
x y 1
5 -9 8 5
2 -4 3 2

Solving by Cross multiplication method:

or, x/[(5)(-4)-(2)(-9)] = y/[(-9)(3)-(8)(-4)] = 1/[(8)(2)-(5)(3)]

or, x/(-20+18) = y/(-27+32) = 1/(16-15)

or, x/(-2) = y/(5) = 1/(1)

We can write:
or, x/(-2) = 1/(1)
or, x = -2

or, y/(5) = 1/(1)
or, y = 5

Answer : x= -2 and y=5