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. The given system of equations is:
2x = -18y + 16 ..............(1)
x + 9y = 8 .................(2)
We can solve this system of equations using any method such as substitution, elimination, or graphing. Let's solve it using the elimination method.
Multiply equation (2) by 2 to eliminate x:
2(x + 9y) = 2(8)
2x + 18y = 16 ...........(3)
Now we have two equations:
2x = -18y + 16 .........(1)
2x + 18y = 16 .........(3)
If we subtract equation (1) from equation (3), we get:
(2x + 18y) - (2x) = 16 - (-18y + 16)
18y = -18y
18y + 18y = 0
36y = 0
y = 0/36
y = 0
Now substitute the value of y = 0 into equation (2):
x + 9(0) = 8
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 0. This represents a unique solution since it is only one ordered pair (x, y) that satisfies both equations.
Therefore, the system of equations has one unique solution.