Hello

(20/19, 45/19) is the intersection point of both lines

For lines

3x + 5y = 15               ...(1)

5x + 2y = 10               ...(2)

For equation (1)

3x + 5y = 15

3x = 15 - 5y

x = (15 - 5y)/3

Putting value of x in (2)

5x + 2y = 10

5 × (15 - 5y)/3 + 2y = 10

Multiplying by 3 both sides

3 × 5 × (15 - 5y)/3 + 3 × 2y = 3 × 10

5(15 - 5y) + 6y = 30

5(15) - 5(5y) + 6y = 30

75 - 25y + 6y = 30

75 - 19y = 30

 75 - 30 = 19y

45 = 19y

19y = 45

y = 15/19 

Now, putting y = 15/19 in (1)

3x + 5y = 15

3x + 5(15/19) = 15

3x + 75/19 = 15

3x = 15 - 75/19

3x = (15 × 9 - 75)/19

3x = (135 - 75)/19

3x = 60/19

x = 60/(19 x 3)

x = 20/19

So, point is (20/19, 45/19)