Question

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

2x + y – 35 = 0, 3x + 4y – 65 = 0

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

2x + y = 35, 3x + 4y = 65

Answer 1

The given equations may be written as:

2x + y – 35 = 0   ...(i)

3x + 4y – 65 = 0   ...(ii)

Here a₁ = 2, b₁ = 1, c₁ = –35, a₂ = 3, b₂ = 4 and c₂ = –65

By cross multiplication, we have:

∴ `x/((1 xx (-65) -4 xx (-35)]) = y/([(-35) xx 3 -(-65) xx 2]) = 1/([2 xx 4 - 3 xx 1])`

⇒ `x/((-65 + 140)) = y/((-105 + 130)) = 1/((8 - 3))`

⇒ `x/75 = y/25 = 1/5`

⇒ `x = 75/5 = 15, y = 25/5 = 5`

Hence, x = 15 and y = 5 is the required solution.