Question

Solve for x and y:

3x – 5y – 19 = 0, –7x + 3y + 1 = 0

Answer 1

The given system of equation is:

3x – 5y – 19 = 0   ...(i)

–7x + 3y + 1 = 0   ...(ii)

On multiplying (i) by 3 and (ii) by 5, we get:

9x – 15y = 57   ...(iii)

–35x + 15y = –5   ...(iv)

On subtracting (iii) from (iv) we get:

–26x = (57 – 5)

–26x = 52

⇒ `x = 52/(-26)`

⇒ x = –2

On substituting the value of x = –2 in (i), we get:

–6 – 5y – 19 = 0

⇒ 5y = (–6 – 19)

⇒ 5y = –25

⇒ `y = (-25)/5`

⇒ y = –5

Hence, the solution is x = –2 and y = –5.