pls.,.answer
2007-03-04 03:34:55 · 3 answers · asked by only me., 1 in Science & Mathematics ➔ Mathematics
On a cartesian plane:
the two linear equations in two variables (usually called X and Y) describe a line (hence linear).
The solutions of these two lines (ie where they share the same points) can be of 3 types:
(1) No solution
- the lines are parallel
y = 2x -5
y = 2x +4
are parallel lines with slope 2 and y-intercept (passing through y axis ie. x = 0) at (0,-5) and (0,4) respectively ... hence no shared points and no solutions
(2) Infinite solutions
- the two lines are the same line. All of their points are shared
y = (5 - 3x)/9
x + 3y = 5/3
are actually the same line. All points P(x,y) satisfying the first equation will satisfy the second equation
(3) One solution
- the two lines cross at one point
y = 2x + 5
y = x - 1
... are two lines of different slope and with different y intercepts. They will cross at a point that can be determined algebraically.
x - 1 = 2x+5
x = -6
y = -7
P(-6,-7) will be their intersection (and hence their solution)
2007-03-04 03:42:36 · answer #1 · answered by Orinoco 7 · 1⤊ 0⤋
Well, that would be three types, depending on the form.
If you are considering independent and consistent systems, there would only be 1 solution for the system.
If you are considering independent and inconsistent systems, there would be no solution.
If you are considering dependent and consistent systems, there would be an infinite number of solutions.
An independent system is a set of two lines, which when plotted on the same Cartesian plane are distinct from each other. Dependent, on the other hand, refers to a set of two lines which has the same graph. Sometimes we refer to it as overlapping lines.
A consistent system is a set of two lines that are able to intersect with each other, at least once. Inconsistent lines do not intersect, ever (they are parallel).
2007-03-04 11:45:31 · answer #2 · answered by Moja1981 5 · 0⤊ 0⤋
Two linear Equations in two variables can ve
a)infintely many solutions if they are linearly dependent.( one is multiple of the other)
b)single uniquesolution if they are linearly dependent
c)no solution if they are (i forgot the term... a solution does not exist if they are parallel)
2007-03-04 11:43:10 · answer #3 · answered by Anonymous · 0⤊ 0⤋