Systems of equations - elimination 7x+8y=20 7x-y=29

First, isolate y in 7x-y=29 because 1 is y's coefficient.
7x-y=29
-y=29-7x
y=7x-29
Now, substitute 7x-29 for y in 7x+8y=20.
7x+8y=20
7x+8(7x-29)=20
7x+56x-232=20
Add all coefficients.
63x-232=20
Isolate x by adding 232 to both sides.
63x-232=20
63x=252
x=4
Now, substitute 4 for x in your first equation.
y=7x-29
y=7(4)-29
y=28-29
y=-1
Your answer would be (4,-1).
Any questions you may have, please contact me or comment.

→ Let me solve your system of equations by elimination.
 
→ Step 1( 7x - y = 29 ) -1 ( 7x + 8y = 20 ) Multiply the second equation by -1

→ Becomes: (7x - y = 29) ( - 7x - 8y = -20)

→ Add both equations to eliminate x: - 9y = 9

→Then solve - 9y = 9 for y, Divide both sides by -9
(- 9y ÷ ( - 9) ) = ( 9 ÷ (-9) )
y = - 1

Now solve for x and to do that, plug it back in to solve for x but first write down the original equation: 
7x - y = 29

→Subtitute -1 for y in 7x - y = 29: 
7x - (-1) = 29 
7x +1 = 29 (simplify both sides of the equation)
7x + 1 + (-1) = 29 + (-1) (Add - 1 to both sides) 
7x = 28 
7x ÷ 7 = 28 ÷ 7 ( Divide both sides by 7)
x = 4
 
→To Check
7 ( 4) - (-1) = 29                      7 ( 4) + 8 (-1) = 20                                
28 - (-1) = 29                          28 + (-8) = 20
29 = 29 :)                               20 = 20 :)

{Hope that helps}