Question

Is the given system of linear equation consistent (_,_), inconsistent or dependent 6x +2y =-4 and 6x +3y =-3

Answer 1

Any math tutors available

Answer 2

A system is said to be consistent if it has a unique solution or an infinite number of solutions. A system is inconsistent if it has no solutions.

Answer 3

The system is consistent and has the solution: x = -1 y = 1

Answer 4

two linear equations in two variables
a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0
a1 b1
will be consistent ( i.e have a unique solution) if ----- ╪ ----
a2 b2

a1 b1 c1
will be inconsistent (i.e. have no solution) if ---- = ----- ╪ -----
a2 b2 c2

a1 b1 c1
will be dependent (i.e. have infinite solutions) if ----- = ----- = -----
a2 b2 c2

Answer 5

6x +2y =-4 and
6x +3y =-3

In case of yr equations

a1 6
---- = ----- = 1
a2 6

b1 2
---- = -----
b2 3

c1 4
---- = -----
c2 3

Answer 6

since a1 b1
----- ╪ ----
a2 b2

so it is a consistent pair of equations

Answer 7

Note that even dependent system is consistent....

Answer 8

Let me say that it is much less messy if you approach systems of linear equations using linear algebra. You can show that a system of linear equations is equivalent to
Ax = b where A is a matrix consisting of the coefficients of the system, x is the unknown and b is the vector in the target space.

The problem boils down to the question, is there a vector x such that the image of x under the transformation A is b. If a vector or a set of vectors exist the system is said to be consistent.

Row reduction, which is kernel preserving (solution preserving) can be used to find the solution set.

Answer 9

@Alchemista
I beg to differ........☺
if u are moderately good in maths, u can easily calculate the ratios and decide........

Answer 10

Gaussian elimination is efficient and obviously for larger systems you will be using that approach anyways.

Answer 11

yes for LARGER systems...........☺