8x-3y= - 12 y-4= - 8
one solution , no solutions or infinite number of solutions ?
then how to classify as consistent independent, consistent dependent or inconsistent
I will assume you meant to type 2 equations
8x-3y= - 12 and
y-4= - 8
well, the second tells you that y = -4
sub into the first:
8x - 3(-4) = -12
x = -24
so what do you think?
yes it is two diff equations
one solution with consistent independent ?
To determine the number of solutions for the given system of equations, we can solve it algebraically using the method of substitution or elimination.
1. Substitution Method:
Let's solve the second equation for y:
y - 4 = -8
Adding 4 to both sides:
y = -4
Now substitute the value of y in the first equation:
8x - 3y = -12
8x - 3(-4) = -12
8x + 12 = -12
Subtracting 12 from both sides:
8x = -24
Dividing by 8:
x = -3
Thus, the solution of the system is x = -3 and y = -4.
Since we obtained unique values for both x and y, we can conclude that the system has one solution.
2. Classification of Consistency:
Using the substitution method, we have found a unique solution for the given system of equations. This implies that the system is consistent.
To determine whether the system is dependent or independent, we can compare the coefficients of x and y in both equations.
8x - 3y = -12 1y - 0x = -4
If the coefficients for both x and y were proportional (e.g., 2x - 6y = -24 and 4x - 12y = -48), the system would be dependent, indicating an infinite number of solutions. However, in this case, the coefficients are not proportional.
Since the coefficients are not proportional and we have a unique solution, we can classify the system as consistent and independent.