Question

7x-8y=40
8y-7x=-40

What is the solution?
Consistent or not?
Dependent or not?

Answer 1

I think that they are consistent

Answer 2

7 -8 |40
8 -7|-40 //-8/7*R1 + R2 -> R2

7 -8 |40
0 9.14 | -85.7

rank(A) = 2
rank(A|B) = 2
n = 2

so its consistent

Answer 3

so the solution is 2

Answer 4

no, the rank of matrix is 2
so is the system consistent

Answer 5

so can we find out what th solution is and if it is dependent or not

Answer 6

so is the solution infinitely, a point or no solution is my question also

Answer 7

http://en.wikipedia.org/wiki/System_of_linear_equations#Solving_a_linear_system

u check the rank of coefficient matrix A and the rank of augmented matrix A|B

if (rank(A) == rank(A|B) != col_num of A)
there is infinte solutions (parametric solution)

if (rank(A) == rank(A|B) == col_num of A)
there is one solution

if (rank(A) != rank(A|B) )
there is no solution

Answer 8

ok

Answer 9

both your eqns are the same with a sign change. thus, ur system of eqns reduce to only one eqn i.e. either 7x-8y=40 or -7x+8y=-40.
thus, we can write 7x=8y+40
which gives x=(8y+40)/7. which means take any value of y and u get the corresponding value of x. Now how many values of y are possible? i assume y is real; hence infinite. thus ur sys of eqn is consistent with infinite solns.
Another rule wud be :
if a1x+b1y=c1 and a2x+b2y=c2, then if
a1/a2=b1/b2=c1/c2 then solns are infinite.