Question

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

6x – 5y – 16 = 0, 7x – 13y + 10 = 0

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

6x – 5y – 16 = 0, 7x – 13y + 10 = 0

Answer 1

The given equations are:

6x – 5y – 16 = 0   ...(i)

7x – 13y + 10 = 0   ...(ii)

Here a₁ = 6, b₁ = –5, c₁ = –16, a₂ = 7, b₂ = –13 and c₂ = 10

By cross multiplication, we have:

∴ `x/([(-5) xx 10 -(-16) xx (-13)]) = y/([(-16) xx 7 - 10 xx 6]) = 1/([6 xx (-13) - (-5) xx 7])`

⇒ `x/((-50 - 208)) = y/((-112 - 60)) = 1/((-78 + 35))`

⇒ `x/((-258)) = y/((-172)) = 1/((43))`

⇒ `x = (-258)/(-43) = 6, y = (-172)/(-43) = 4`

Hence, x = 6 and y = 4 is the required solution.