What is the solution to this system?

5x + y = 8
11x + 7y = -4

5x + y = 8
Multiply this equation by 7, 
35x + 7y = 56   first equation
11x + 7y = -4     second equation, 

Compare both the equation, Subtract 2nd one from 1st, 
24x = 60
x = 60/24
x = 5/2

Substitute the value of x in very-first equation, 
5(2.5) + y = 8
y = 8 - 12.5
y = -4.5

In short, Answers are: x = 2.5 and y = -4.5

(Remember, i have used "elimination method" you can also use other methods like substitution method, but answer wouldn't change)!

Hope this helps!

We are going to solve this by elimination:

5x + y = 8          (i)

11x + 7y = -4  (ii)

Multiply equation (i) by 7

7*(5x + y)  = 7*(8)

35x + 7y = 56 (iii)

Comparing equations (ii) and (iii)

11x + 7y = -4  (ii)
                                                                   (ii)  minus (iii)
35x + 7y = 56 (iii)

-24x + 0y = -60

-24x = -60

x = -60/-24

x =-5/2

x = -2.5

Recall:

11x + 7y = -4  (ii)

11*2.5 + 7y = -4

27.5 + 7y = -4

7y = -4 - 27.5

7y = -31.5

y = -31.5/7

y = - 4.5

Therefore  x = 2.5 and y = -4.5.

Hope this explains it.