Determine whether the system is consistent, inconsistent, or dependent.
3x - 3y = -9
9x - 9y = -27
3x-3y=-9 /*-3
-9x+9x=+27
9x-9y=-27
If you look at the top, the equotations answer after solving will be 0=0 and this is mean DEPENDENT.
To determine whether the system is consistent, inconsistent, or dependent, we can compare the coefficients of the variables in both equations. Specifically, we need to check if the ratios of the coefficients are equal for both equations.
Let's take the two equations of the system:
Equation 1: 3x - 3y = -9
Equation 2: 9x - 9y = -27
We'll first transform both equations to have the same coefficient for the variables.
Multiply Equation 1 by 3 to make the coefficients equal:
Equation 1 (after multiplication): 9x - 9y = -27
Now let's compare the two equations once again:
Equation 1: 9x - 9y = -27
Equation 2: 9x - 9y = -27
Here, we can observe that the coefficients of both variables (x and y) are the same in both equations. Therefore, the ratios of the coefficients are also equal.
This means that the two equations represent the same line on the coordinate plane. In other words, the system is dependent, since one equation can be obtained by simply multiplying the other equation by a constant.
In conclusion, the system is dependent.