5 х + 12y - 10 = 0

2x - 3y + 35 = 0

( - 10, 5)

Step-by-step explanation:

Given the 2 equations

5x + 12y - 10 = 0 (add 10 to both sides)

5x + 12y = 10 → (1)

2x - 3y + 35 = 0 (subtract 35 from both sides)

2x - 3y = - 35 → (2)

Multiplying (2) by 4 and adding to (1) will eliminate the y - term

8x - 12 y = - 140 (3)

Add (1) and (3) term by term

5x + 8x + 12y - 12y = 10 - 140, that is

13x = - 130 (divide both sides by 13)

x = - 10

Substitute x = - 10 into either (1) or (2) and solve for y

Substituting in (1)

5 ( - 10) + 12y = 10

- 50 + 12y = 10 (add 50 to both sides)

12y = 60 (divide both sides by 12)

y = 5

Solution is ( - 10, 5)