How do I solve using the elimination method???

add the equations together

7x = 28

that eliminates the y -variable

x = 4

plug back in to one of the eq

2(4) -y = 6

y =2

7x = 28
x = 4

20 + y = 22
y = 2

x = 4 , y = 2

2x-y=6
-> 2x-6=y

5x+y=22 , y=2x-6
5x+2x-6=22
-> 7x=28
->x=4
y=2x-6 ->y=2*4-6=2

2x - y = 6
5x + y = 22

(2x - y) + (5x + y) = 6 + 22
7x = 28
x = 28/7
x = 4

5x + y = 22
5(4) + y = 22
20 + y = 22
y = 22 - 20
y = 2

x = 4
y = 2

2x - y = 6
5x + y = 22

2x - y = 6
5(2x - y) = 5(6)
10x - 5y = 30

5x + y = 22
2(5x + y) = 2(22)
10x + 2y = 44

...10x - 5y = 30
--10x + 2y = 44
----------------------- (substraction)
-7y = -14

-7y = -14
y = -14/-7
y = 14/7
y = 2

2x - y = 6
2x - 2 = 6
2x = 6 + 2
2x = 8
x = 8/2
x = 4

∴ x = 4 , y = 2

7x=28
x=4

8-y=6
y=2