To determine the number of solutions the system of equations has, we need to find the determinant of the coefficients of x and y in the system.
The determinant can be found using the formula:
det = ad - bc
where a, b, c, and d are the coefficients of the system.
In this case, the coefficients are:
a = 2
b = -2
c = 17
d = -12
Calculating the determinant:
det = (2)(-12) - (-2)(17)
= -24 + 34
= 10
Since the determinant is non-zero (10 ≠ 0), the system of equations has a unique solution. Therefore, the system has exactly one solution.
How many solutions does the system of equations below have?
2x − 2y = 5
17x − 12y = 16
1 answer