The given system of equations is:
12x - 15y = 18 (Equation 1)
4x - 5y = 6 (Equation 2)
To determine the number of solutions, we can solve the system using any method. Let's use the method of substitution.
From Equation 2, we can express x in terms of y:
4x - 5y = 6
4x = 5y + 6
x = (5y + 6)/4 (Equation 3)
Now substitute Equation 3 into Equation 1:
12x - 15y = 18
12((5y + 6)/4) - 15y = 18
(30y + 36)/4 - 15y = 18
30y + 36 - 60y = 72
-30y = 36
y = -36/30
y = -6/5
Substitute the value of y into Equation 3 to find x:
x = (5(-6/5) + 6)/4
x = (-6 + 6)/4
x = 0/4
x = 0
Therefore, the system has one solution, x = 0 and y = -6/5.
How many solutions does the system have? 12x−15y=18 4x−5y=6(1 point) Responses no solution no solution infinitely many solutions infinitely many solutions one solution one solution two solutions
1 answer
1 answer