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helpfulAnswer:
a. (1/2)x - 5y = 10Step-by-step explanation:
Let us consider the two equations to be :
ax + by = c
Ax + By = C
Now, for the system of equations to have infinitely many solutions :
a/A = b/B = c/C
So, for the given system of equations :
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
a/A = (1/2)/(-1/2) = -1
b/B = (-5/5) = -1
c/C = 10/(-10) = -1
Thus, it is correct.
b. 7x + 2y = -14
-7x + 2y = -14
a/A = 7/-7= -1
b/B = 2/2 = 1
c/C = -14/-14 = 1
Thus, it is not correct.
c. x + 6y = -18
x - 6y = 18
a/A = 1/1 = 1
b/B = 6/-6 = -1
c/C = -18/18 = -1
Thus, it is not correct.
d. (3/4)x - 9y = 12
(-3/4)x + 9y = 12
a/A = (3/4)/(-3/4) = -1
b/B = -9/9 = -1
c/C = 12/12 = 1
Thus, it is not correct.
Hence, correct option is :
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
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