is -2x-y=9, 3x-4y=-8 dependent, independent, or inconsistent
so which one is it. dependent or independent?
To determine if the system of equations -2x - y = 9 and 3x - 4y = -8 is dependent, independent, or inconsistent, we can solve the system using one of the methods, such as substitution or elimination. Let's use the elimination method.
We need to eliminate one variable by manipulating the equations so that when we add or subtract them, one of the variables cancels out. Let's multiply the first equation by 3 and the second equation by -2 to make the coefficient of x the same:
Equation 1: -2x - y = 9 (Multiply both sides by 3)
Equation 2: 6x - 8y = 16 (Multiply both sides by -2)
Now, let's add the two equations together:
(-2x - y) + (6x - 8y) = 9 + 16
4x - 9y = 25
We now have a new equation: 4x - 9y = 25.
Since we have obtained a new equation that does not involve any of the original variables (x and y), the system is independent. The solution to this system is a unique pair of values for x and y.
Therefore, the answer is that the system of equations -2x - y = 9 and 3x - 4y = -8 is independent.