(B) -2x+4y=18 and 4x-8y=-36 has infinitely many solutions.
What is Solution of Equations?
The values of variables which satisfy the system of equations togetherly.
If two equations are ax+by=c and dx+ey=f then it has infinitely many solutions if [tex]\frac{a}{d}=\frac{b}{e}=\frac{c}{f}[/tex].
Option (A):
a/d = -4/4 = -1
b/e = 6/-3 = -2
Since [tex]\frac{a}{d}\ne\frac{b}{e}[/tex] so it cannot be choice.
Option (B):
a/d = -2/4 = -1/2
b/e = 4/-8 = -1/2
c/f = 18/-36 = -1/2
so it is the correct choice.
Option (C):
a/d = 3/-6 = -1/2
b/e = -2/-4 = 1/2
So it is not the choice.
Option (D):
a/d = 5/15 = 1/3
b/e = -3/-9 = 1/3
c/f = 12/24 = 1/2
So it is also cannot be choice.
Hence the correct choice which have an infinitely many solution is (B) -2x+4y=18; 4x-8y=-36.
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