how do you know when an equation has infinate many solutions and how do you know if an equation has no solutions?
The second part of this question I get. If you work an equation and come up with 5=3 this is not a solution. Is that part right? I guess I do not understand the question.
3 answers
For your second question, yes.
Let me see if I get the first part. If you have an equation and the solution is correct, then how does this make it infinate? Does this mean any integer you substitute for the variable will work? Can you explain this to me?
for the first part,, sorry, i am not sure about this,, if you only have ONE given equation for instance,, sin(x)=1 ==> the solution for this is x = pi*2+k*2pi, for k greater than or equal to zero (note: pi/2 is in radians which is also equal to 90 degrees), therefore sin x = 1 has infinitely many solutions,,
another example if only one equation is given is 1/x=0 ,,here no real value of x will satisfy this, thus it has no solution.
if you have TWO given LINEAR equations, check if they are parallel, intersecting, or coinciding,,
*if parallel==> no solution since they will never intersect
[for an equation, Ax+By=C, two equations are parallel if their respective A and B are equal
ex: 2x-5y=3 and 2x-5y=-8]
*if intersecting==> one unique solution, since they will intersect at one point
*if coinciding ==> infinitely many solutions since the two given equations are equal
[for an equation, Ax+By=C, two equations are coinciding if their respective A and B are the multiple of the other
ex: 3x-5y=4 and 6x-10y=8
so there,, i hope i was able to help you.. =)
another example if only one equation is given is 1/x=0 ,,here no real value of x will satisfy this, thus it has no solution.
if you have TWO given LINEAR equations, check if they are parallel, intersecting, or coinciding,,
*if parallel==> no solution since they will never intersect
[for an equation, Ax+By=C, two equations are parallel if their respective A and B are equal
ex: 2x-5y=3 and 2x-5y=-8]
*if intersecting==> one unique solution, since they will intersect at one point
*if coinciding ==> infinitely many solutions since the two given equations are equal
[for an equation, Ax+By=C, two equations are coinciding if their respective A and B are the multiple of the other
ex: 3x-5y=4 and 6x-10y=8
so there,, i hope i was able to help you.. =)
1 answer