solve by the elimination method.

what is the solution of the system?
type a pair, an integer or a fraction, N if no solution, and I for many solutions.

Q:
x + 8y = 17
-x + 2y = 3

A: N?

To solve the system of equations using the elimination method, we will add the equations together to eliminate the x variable.

Adding the equations:
(x + 8y) + (-x + 2y) = 17 + 3
8y + 2y = 20
10y = 20
y = 2

Now substitute the value of y back into one of the original equations:

-x + 2(2) = 3
-x + 4 = 3
-x = 3 - 4
-x = -1
x = 1

Therefore, the solution to the system of equations is the ordered pair (x, y) = (1, 2).

To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.

Let's start by eliminating the variable "x". To do this, we can add the two equations together:

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

Simplifying the equation, we combine like terms:

10y = 20

Now we can solve for "y" by dividing both sides of the equation by 10:

y = 2

Now that we have the value of "y", we can substitute it back into one of the original equations to solve for "x". Let's use the first equation:

x + 8(2) = 17

Simplifying the equation:

x + 16 = 17

Subtracting 16 from both sides:

x = 1

Therefore, the solution to the system of equations is the ordered pair (1, 2).

However, upon closer inspection, we can see that the two original equations are contradictory. The first equation states that when x is positive (1), y should be positive, while the second equation states that when x is positive (1), y should be negative. Therefore, there is no solution to the system, denoted as "N".