Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.

8x + 7y = 39

4x - 14y = - 68

First, let's multiply the first equation by two on the both sides:

8x + 7y = 39 / 2

⇒ 16x + 14y = 78

Now, the system is:

16x + 14y = 78

4x - 14y = - 68

After adding this up in the column:

(16x + 4x) + (14y - 14y) = 78 - 68

20x = 10

⇒ x = 10/20 = 1/2

y can be calculated by replacin the x:

8x + 7y = 39

⇒ 8 · 1/2 + 7y = 39

4 + 7y = 39

7y = 39 - 4

7y = 35

⇒ y = 35 : 7 = 5