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

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2x + 3y = 8........(1)

x+ 8y = 17.........(2)

using the elimination method, we will multiply (2) by -2 and then add to (1):

==> 2x + 3y = 8

==> -2x - 16y = -34

Now add both equations:

==> -13y = - 26

Now divide by -13

**==> y= 2**

Now to find x, we will substitute in (1):

2x+ 3y = 8

2x + 3*2 = 8

==> 2x = 2

**==> x= 1**

2x+3y = 8.....(1)

x+8y = 17.......(2)

To solve the equation we eliminate x :

Eq(1) -2*eq(2) gives:

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

3y-16y = 8-34

-13y = -26.

y = -26/-13 = 2.

Now put y = 2 in eq (2):

x+8*2 = 17

x = 17-8*2 = 17-16 = 1.

Therefore x = 1 and y = 2.

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**