Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + 2y = 0
2x + 4y = 0



one solution

no solution

coincident

Answer 1

x = -2y .

2 ( -2y ) + 4 (-2y) = 0

-4y - 8y = 0

-12y = 0

y = 0 / -12 = 0 .

x = -2 ( 0 ) = 0 .

The solution has one point.

Plus, if the equation is "Linear" i.e with the highest degree being 1 , there will most likely be only "one" solution.

Answer 2

x + 2y = 0
2x + 4y = 0

If you multiply both sides of the first equation by 2, you get the second equation.
Therefore, there are infinitely many solutions. Anything that satisfies either equation satisfies the other one too.

Answer 3

But tiana, then why is my solution wrong ?

Answer 4

Replace 2 for x and -1 for y
(2)+2(-1) =0
2(2)+4(-1)=0

2) Check if they work
2-2=0 Correct
4-4=0 Correct