solve the system 2x + 3y = 8 x + 8y = 17

We'll solve the system of equations using the elimination
method, also:

2x+3y= 8
(1)

x+8y= 17 (2)

We'll
multiply (2) by -2:

-2x - 16y =
-34 (3)

We'll add (3) to
(1):

2x + 3y - 2x - 16y = 8 -
34

We'll combine like
terms:

-13y = -26

We'll divide
by -13 both sides:

y =
2

We'll substitute y = 2 in
(2):

x+8y= 17

x + 16 =
17

We'll subtract 16 both
sides:

x = 17 -
16

x =
1

The solution
of the given system is {(1 ,
2)}.

We
could also use the substitution method. We'll write x with respect to y, from the
equation (2).

x+8y=
17

x = 17 - 8y (3)

We'll
substitute x in (1):

2(17 - 8y)+3y=
8

We'll remove the
brackets:

34 - 16y + 3y =
8

We'll combine like
terms:

-13y = 8 - 34

-13y =
-26

We'll divide by
-13:

y =
2

We'll substitute y in
(3):

x = 17 -
16

x =
1