Determine if f could be a linear function
x 0 1 2 3 4
f(x) 3 5 7 11 15
is this a linear function
and then...
2x - 6y = 12
3x-9y = -27
What is the solution of the system of equations? A) no solution B) a point C) infinitely many solutions
Is the system consistent or inconsistent
Are the equations dependent or independent...
Thank you so much if you could help me out
1) no it is not linear.
2) The lines in the equations are parallel.
They are dependent, consistent, no solution.
Juan solved the system of linear equations 8x-3y=-1 and -5x+2y=1
To determine if a function is linear, we need to check if the difference between consecutive y-values is constant.
For the first set of data points:
x: 0 1 2 3 4
f(x): 3 5 7 11 15
The differences between consecutive y-values are:
5-3 = 2
7-5 = 2
11-7 = 4
15-11 = 4
As we can see, the differences between consecutive y-values are not constant. Therefore, the function f cannot be a linear function.
Moving on to the system of equations:
2x - 6y = 12
3x - 9y = -27
We can solve this system of equations to determine the type of solution.
To do that, let's use the method of elimination:
First, we can multiply the second equation by 2 to make the coefficients of x in both equations the same (6x):
2x - 6y = 12
6x - 18y = -54
Now, we subtract the first equation from the second equation to eliminate x:
(6x - 18y) - (2x - 6y) = (-54) - 12
4x - 12y = -66
Simplifying the equation:
4x - 12y = -66
Dividing all terms by 4:
x - 3y = -16.5
From this result, we can see that the variables have not canceled out and we are left with a non-zero coefficient for both x and y. Therefore, the system has a unique solution (a point), which means the solution to the system of equations is B) a point.
Next, we can determine the consistency of the system. A system is consistent if it has at least one solution, and it is inconsistent if it has no solutions.
Since we have found that the system has a unique solution (a point), the system is consistent.
Finally, let's determine if the equations are dependent or independent. Two equations are dependent if they are multiples of each other or represent the same line. Two equations are independent if they are not multiples of each other and represent different lines.
Looking at the two equations:
2x - 6y = 12
3x - 9y = -27
We can see that the coefficients of x and y are not proportional. Therefore, the equations are independent.
In summary:
- The first set of data points does not represent a linear function.
- The system of equations has a unique solution (a point) and is consistent.
- The equations are independent.