Solve the system using 2 methods. x+2y=6 2x+6y=8

The first method is the substitution method.

We'll write one variable depending on the other one.

From the first equation, we'll choose to write x=6-2y

Now we'll substitute x from the second equation, by it's expression and we'll get an expression in y.

2(6-2y)+6y=8

12-4y+6y=8

12+2y=8

We'll subtract 12 both sides:

2y=8-12

2y=-4

y=-2

Now, we'll substitute y in the x expression.

x=6-2y

x=6+4

x=10

The second method is to reduce one variable from the both equations of the system.

We'll reduce x and for this reason, we'll multiply the first equation by -2 and we'll get.

-2x-4y=-12

Now we'll add the new equation to the second one.

-2x-4y+2x+6y=-12+8

2y=-4

y=-2

x=10