x - y = 3
2x = 2y + 6
The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many
2006-12-11 15:54:19 · 14 answers · asked by Amuthan A 1 in Science & Mathematics ➔ Mathematics
Multiply the first equation throughout by 2 and add 2y to both sides to get the second equation. The system of equations effectively reduces to x=y+3. Now, for any given number y, we can find x=y+3. So there are infinitely many x and y's satisfying the relation.
Ans(E):Infinitely many.
For ex. (3,0),(4,1),(5,2),(6,3),(3 1/2,1/2).................
2006-12-11 16:07:05 · answer #1 · answered by Anonymous · 0⤊ 0⤋
(E) Infinitely many
This is because both equations are telling the same story and so in effect you only have one equation with 2 unknowns. The solutions fit on a straight line when graphed ... there being an infinite number of them
2006-12-11 23:56:56 · answer #2 · answered by Wal C 6 · 0⤊ 0⤋
First set both eqns into standard form:
x-y=3
2x-2y=6
Now do you see that the second line is a multiple of the first one? That means they are the same line. This means that there are infinitely many solutions to this system of eqns.
2006-12-11 23:57:35 · answer #3 · answered by AibohphobiA 4 · 0⤊ 0⤋
The answer is none (A) because the second equation and the first equation are the same equation. You need a 2nd unrelated equation to solve for x and y.
The second equation is
2x = 2y + 6
2x - 2y = 6 divide by 2
x - y = 3 which is the same as the first equation.
2006-12-11 23:56:50 · answer #4 · answered by rscanner 6 · 0⤊ 0⤋
As both the equations are resolved to be one and the same, they boil down to the form of a straight line with infinite points, albeit solutions i.e. the answer is E.
2006-12-12 05:58:29 · answer #5 · answered by pravkas 2 · 0⤊ 0⤋
it has infinitely many solutions.consider each equation as a line in 2-d plane then the two lines coincide hence infinitely many solutions.
2006-12-12 00:44:03 · answer #6 · answered by ranjith 1 · 0⤊ 0⤋
First set each equation equal to y
y=x-3
y=x-3
If they are the same lines then there are Infinitely many solutions
2006-12-12 00:00:26 · answer #7 · answered by TheThing 2 · 0⤊ 0⤋
E
Divide the second equation by 2 and you'll get the first equation.
y can be any value, so x is that value plus 3.
2006-12-11 23:56:07 · answer #8 · answered by Anonymous · 0⤊ 0⤋
Answer is (A) None.
Because
1. if you substitue x=y+3 in the above equation you will get answer 0.
2. if you substitue y=x-3, also you will get answer 0.
so the final answer is No solution for this question.
2006-12-12 00:00:08 · answer #9 · answered by AB_SVN_YZ 1 · 0⤊ 0⤋
you have the second equation reduced to the first when simplified. U have effedtively one equation with two variables.
So infinte solutions
2006-12-12 00:06:12 · answer #10 · answered by HeL!0$ 2 · 0⤊ 0⤋