Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
![6x+y=-1\\y=-6x-1](https://tex.z-dn.net/?f=6x%2By%3D-1%5C%5Cy%3D-6x-1)
second equation:
![-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1](https://tex.z-dn.net/?f=-6x-4y%3D4%5C%5C-6x%3D4y%2B4%5C%5C-6x-4%3D4y%5C%5Cy%3D-%5Cfrac%7B3%7D%7B2%7D%20x-1)
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Answer:
-5 =x
Step-by-step explanation:
f(x)=x+5
Set the function equal to zero
0 = x+5
Solve for x
-5 = x+5-5
-5 =x
(g•h)=g(h(x))
So that means subbing h(x) into g(x) wherever there’s an “x”
So
= 3/ [h(x)-2]
= 3/(9x-2)
Then we sub in the 7
=3/ [9(7)-2]
=3/61
1. X=3, 2. X=4, 3. X= 95/2
Answer:
13-4n
Step-by-step explanation:
The generic formula to calculate this is. a+(n-1) d
“a” is the first term and “d” is the difference in our case “a” is 9 and “d” is -4
9+(n-1)(-4)
9-4n+4
13-4n