Elimination method

-2x+y=-8

2x+4y=18

We have to add first eq to second eq.

-2x+y+2x+4y=-8+18

5y=10 / : 5

y=2

Now we can backsubstitute

2x+4*2=18

2x+8=18 / - 8

2x=18-8

2x=10 / : 2

x=5

Finally we obtain result

x=5

y=2

Elimitation method

basically eliminate one of the terms completely

we see that there is a - 2x and a 2x in the 2 equations

so just add them together

2x-2x+4y+y=18-8

5y=10

divide both sides by 5

y=2

subsitute

-2x+2=-8

subtract 2 form boht sides

-2x=-10

divide both sides by 2

-x=5

multiply - 1

x=5

y=2

x=5