how many solutions does the system have?
x-2y=6
3x-6y=18
a)1
b)2
c)many
d)none
-2y=6-6
-2y=0
y=0 ans.
Proof:
3*6-6*0=18
18+0=18
18=18
One solution: (6,0).
thanks Rezu
If you triple the first equation , you will get the 2nd
so there is only one equation,
and there is an infinite number of solutions.
Rezu gave you only one
here is another (2,2)
and another (0,-3) etc
so infinite or just one?
omg come down it was just a question!
To determine the number of solutions for this system of equations, we can solve it using either the substitution method or the elimination method.
Let's use the elimination method to solve this system:
1) Multiply the first equation by 3:
3(x - 2y) = 3(6)
3x - 6y = 18
2) Notice that the two equations have the same second term (-6y). Subtract the second equation from the first equation to eliminate this term:
(3x - 6y) - (3x - 6y) = 18 - 18
0 = 0
3) The result is 0 = 0, which means the two equations are equivalent. This indicates that the two equations represent the same line rather than two distinct lines.
Since the two equations represent the same line, they intersect at infinite points. Consequently, the system has infinitely many solutions.
Therefore, the answer is:
c) many
come on!
I already gave you more than one.
How many points lie on a straight line??????