anonymous
  • anonymous
7x-8y=40 8y-7x=-40 What is the solution? Consistent or not? Dependent or not?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I think that they are consistent
anonymous
  • anonymous
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
anonymous
  • anonymous
so the solution is 2

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anonymous
  • anonymous
no, the rank of matrix is 2 so is the system consistent
anonymous
  • anonymous
so can we find out what th solution is and if it is dependent or not
anonymous
  • anonymous
so is the solution infinitely, a point or no solution is my question also
anonymous
  • anonymous
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
anonymous
  • anonymous
ok
anonymous
  • anonymous
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.

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