7x-8y=40 8y-7x=-40 What is the solution? Consistent or not? Dependent or not?

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7x-8y=40 8y-7x=-40 What is the solution? Consistent or not? Dependent or not?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I think that they are consistent
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
so the solution is 2

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