A system of equations will always have a solution as long as the number of equations is equal to the number of variables?
2007-04-27 09:54:29 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
no
y = 2x
3y = 6x
has infinite number of solutions, while
y = 2x
y = 2x +1
has no solutions at all
2007-04-27 09:58:57 · answer #1 · answered by iluxa 5 · 2⤊ 0⤋
If you try to solve a dependent system by algebraic methods, you will eventually run into an equation that is an identity. An identity is an equation that is always true, independent of the value(s) of any variable(s). For example, you might get an equation that looks like x = x, or 3 = 3. This would tell you that the system is a dependent system, and you could stop right there because you will never find a unique solution.
2007-04-27 16:59:48 · answer #2 · answered by Robert L 7 · 0⤊ 0⤋
Not necessarily, you need as many equations as you have unknown variables in order to solve those variables. However, there are equations, such as differentials, where although you may have two variables and two equations, the solution to the variables may disagree and produce no solution.
2007-04-27 17:01:41 · answer #3 · answered by Sergio 2 · 0⤊ 0⤋
false, if the equations have the same slope we have parallel lines, therefore no solutions. Or if they are the same equation we have infinitely many solutions.
2007-04-27 17:00:41 · answer #4 · answered by leo 6 · 0⤊ 0⤋
I took a whole course in college(Matrix Algebra) just to be able to give you the answer NO!
2007-04-27 17:05:07 · answer #5 · answered by lahomaokie 2 · 0⤊ 0⤋
Not necessary...it can have one unique, infinitely many, or even no solutions at all.
2007-04-27 17:05:20 · answer #6 · answered by cyclonemagnum 1 · 0⤊ 0⤋
not always
2007-04-27 17:01:48 · answer #7 · answered by kaiser_willi 1 · 0⤊ 0⤋