How many solutions does the system of equations have?
2x = −18y + 16 and x + 9y = 8
To find the number of solutions, we need to solve the system of equations and determine if there is a unique solution, infinitely many solutions, or no solution.
Let's solve the system of equations:
2x = -18y + 16 ---> x = -9y + 8 (equation 1)
x + 9y = 8 (equation 2)
Substitute equation 1 into equation 2:
-9y + 8 + 9y = 8
-9y + 9y + 8 = 8
8 = 8
The equation 8 = 8 is true, which means the original equation 2 has infinitely many solutions.
Therefore, the system of equations has infinitely many solutions.