Identify the solution(s) of the system of equations

9x + 2y = 6
8x - 2y = 8

add the two equations to get

17x = 14

identify the solution(s) of the system of the equations 9x+2y=6 and 8x-2y=8

To find the solution(s) of a system of equations, we can use the method of elimination or substitution. In this case, we can use the method of elimination.

Step 1: Add the two equations together to eliminate the y terms.
(9x + 2y) + (8x - 2y) = 6 + 8
Combining like terms, we get:
17x = 14

Step 2: Solve for x by dividing both sides of the equation by 17.
x = 14 / 17

Step 3: Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation.
9(14 / 17) + 2y = 6
Multiply 9 by (14 / 17):
126 / 17 + 2y = 6
Subtract 126 / 17 from both sides:
2y = 6 - 126 / 17
Multiply 6 by 17/17 to get a common denominator:
2y = (102 - 126) / 17
Simplify the numerator:
2y = -24 / 17

Step 4: Solve for y by dividing both sides of the equation by 2.
y = (-24 / 17) / 2
Simplify:
y = -24 / 34
Reduce the fraction:
y = -12 / 17

So, the solution to the system of equations is:
x = 14 / 17
y = -12 / 17