a) The system has a unique solution for and any value of , and we say the system is consisted
b) The system has infinite solutions for and
c) The system has no solution for and
Step-by-step explanation:
Since we need to base the solutions of the system on one of the independent terms (), the determinant method is not suitable and therefore we use the Gauss elimination method.
The first step is to write our system in the augmented matrix form:
The we can use the transformation , obtaining:
.
Now we can start the analysis:
If then, the system has a unique solution for any value of , meaning that the last row will transform back to the equation as:
from where we can see that only in the case of the value of can not be determined.
if and the system has infinite solutions: this is very simple to see by substituting these values in the equation resulting from the last row:
which means that the second equation is a linear combination of the first one. Therefore, we can solve the first equation to get as a function of o viceversa. Thus, () is called a parameter since there are no constraints on what values they can take on.
if and the system has no solution. Again by substituting in the equation resulting from the last row:
which is false for all values of and since we have something that is not possible the system has no solution
If the regular price of a T-shirt is 10 USD and the store sells off its wares at 80% of its regular price, then the price at which the store would still the aforementioned T-shirt would be 80% of its 10 USD price.
80% of $10 =
0.8 * 10 = $8
This means that the price at which the T-shirt will go for, due to the ongoing sales will be $8.
Also, being asked to find the 10% and 20% of $10 is just as simple
10% of $10 =
0.1 * 10 = $1
20% of $10 =
0.2 * 10 = $2
Therefore, the 10% and 20% of $10 is $1 and $2 respectively.
Slope is rise over run so since it rose 4 and went 1 to the right the slope would be 4 because 4/1=4
P.S. The actual formula for slope is y2-y1 over x2-x1 so it would be 5-1/1-0 which again is 4/1