Question

Solve each of the following systems of equations by the method of cross-multiplication 

2x − y = 6
x − y = 2

Answer 1

The given system of equations may be written as

2x − y - 6 = 0
x − y - 2 = 0

Here 

`a_1 = 2, b_1 = -1, c_1 = -6`

`a_2 = 1, b_2 = -1, c _2 = -2`

By cross multiplication, we get

`=> x/((-1)xx(-2)-(-6)xx(-1)) = (-y)/(2xx(-2)-(-6)xx1)= 1/(2xx (-1) -( -1)xx1)`

`=> x/(2-6) = (-y)/(-4+6)= 1/(-2 + 1)`

`=> x/(-4) = (-y)/2 = 1/(-1)`

`=> x/(-4) = (-y)/2 = 1`

Now

`x/(-4) = -1`

`=> x = (-4) xx (-1) = 4`

And

`(-y)/2 = -1`

`=> (-y) = (-1) xx 2`

=> -y = -2

=> y = 2

Hence, x = 4, y = 2 is the solution of the given system of the equations