Question

How do you solve system of equations and tell if they're consistant and independant,consistant and dependent,and inconsistant?

If you find no solutions then the system is inconsistent.

Suppose you have N variables and M equations (N larger than or equal to M). Then, if you obtain a N-M dimensional solution space, i.e. the solution contains N-M undetermined parameters, the M equations are independent and consistent.

If the dimension of the solution space is larger, then the set of equations is dependent.

Also, if M is larger than N and there are solutions then the equations are dependent.

Thanks for the help but that made no sense to me. This is the problem I have:Choose the correct description of the system of equations. x+2y=7 and 3x-2y=5. I tried to solve it and I got (7,8) and I have to tell if its consistant etc.

If you add the equations you get:

4 x = 12 -->

x = 3

If you insert x = 3 in the first equation you get

2 y = 4 --->

y = 2

We found a solution, so the system of equations is consistent. We have two variables and two equations. N = 2, M= 2 and thus N - M = 0. The solution has no free parameters if the equations are independent. That's the case here.

Answer 1

1.(-1/2,-5/2),(2,5) follow me on instagram famous_jaylan
2.0
3.-1,19
4.-9,9
5.exponential
6.a
7.d
8.c
9.b
10.y=-2x^2+4 is just 4 units up from y=-2x^2

Answer 2

7 and 9 are wrong

Answer 3

The answers are correct i just took the quiz