Given line equations,

5x + 7y = 3 … (i)

2x – 3 y = 7 … (ii)

Now, performing multiplication of (i) by 3 and (ii) by 7, we get

15x + 21y = 9

14x – 21y = 49

On adding we get,

29x = 58

x = 58/29 = 2

Substituting the value of x in (i), we get

5(2) + 7y = 3

10 + 7y = 3

7y = 3 – 10

y = -7/7 = -1

Hence, the point of intersection of lines is (2, -1)

Now, the slope of the line joining the points (2, -1) and (0, 0) will be

m = y₂ – y₁/ x₂ – x₁

= (0 + 1)/ (0 – 2)

= -1/2

Equation of the line is given by:

y – y₁ = m (x – x₁)

y – 0 = -1/2 (x – 0)

2y = -x

Thus, the required line equation is x + 2y = 0.