Question

Solve the system of equations by using the method of cross multiplication:

2x + 5y – 1 = 0, 2x + 3y – 3 = 0

Solve the following system of equations by using the method of cross multiplication:

2x + 5y = 1, 2x + 3y = 3

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 xx (-3) -3 xx (-1)]) = y/([(-1) xx 2 -(-3) xx 2]) = 1/([2 xx 3 - 2 xx 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.