2x-3y= -5 and -4+6y= -10 is the answer INFINITE SOLUTIONS?

Question

I graphed this and graph shows parallel, but when I worked it the answer was 0=0  so I am not sure if it is Infinite Solutions OR No Solution

Answer 1

line 1...6y-4=-10 be a strate line...6y=4-10=-6, so y=-1

horizontal line that go thru (0,-1)

line 2...2x-3y=-5 become 3y=2x+5 or y=(2/3)x+(5/3)...strate line with slope=(2/3)

If yu wanna no weer 2 lines hit, set y=-1

(2/3)x+(5/3) =-1

(2/3)x=-(3/3) -(5/3)=-(8/3)

so x=(3/2)*(-8/3)=-24/6=-4

Answer 2

2x-3y= -5

and -4x+6y= -10

0=0

Since 0=0 is always true, this means that there are an infinite number of solutions.

So the system is consistent and dependent.

Infinite Solutions

Answer 3

Given two lines are: 2x - 3y = -5 and -4x + 6y = -10

Note: Two lines in the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are:

i) Said to be consistent and has an unique solution, if a₁/a₂ is not equal to b₁/b₂

ii) Said to be consistent and has infinitely many solutions, if a₁/a₂ = b₁/b₂ = c₁/c₂

iii) Said to be inconsistent, no solution and parallel, if a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Here in the given set, a₁/a₂ = 2/-4 = -1/2

b₁/b₂ = -3/6 = -1/2

c₁/c₂ = -5/-10 = 1/2

Thus we have a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Hence, the two lines given by the equations have no solution; inconsistent and

parallel.