Question

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

3x – 2y + 3 = 0, 4x + 3y – 47 = 0

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

3x – 2y + 3 = 0, 4x + 3y – 47 = 0

Answer 1

The given equations are:

3x – 2y + 3 = 0   ...(i)

4x + 3y – 47 = 0   ...(ii)

Here a₁ = 3, b₁ = –2, c₁ = 3, a₂ = 4, b₂ = 3 and c₂ = –47

By cross multiplication, we have:

∴ `x/([(-2) xx (-47) -3 xx 3]) = y/[(3 xx 4 -(-47) xx 3]) = 1/([3 xx 3 -(-2) xx 4])`

⇒ `x/((94 - 9)) = y/((12 + 141) ) = 1/((9 + 8))`

⇒ `x/((85)) = y/((153)) = 1/((17))`

⇒ `x = 85/17 = 5, y = 153/17 = 9`

Hence, x = 5 and y = 9 is the required solution.