Answer:
[tex]\large \boxed{\sf \ \ 69 \ \textbf{touchdowns } 11 \ \textbf{field goals } \ }[/tex]
Step-by-step explanation:
Hello,
Touchdown is 7 points, field goals is 3 points
Let's note a the number of touchdowns and b the number of field goals, we can write
  (1)   a + b = 80
  (2)   7a + 3b = 516
(2) - 3*(1) gives
7a + 3b - 3(a + b) = 516 - 3*80
<=> 7a + 3b -3a - 3b = 516 - 240 = 276
<=> 4a = 276
<=> [tex]a=\dfrac{276}{4}=69[/tex]
And then from (1) b = 80 - 69 = 11
Hope this helps
