Mathematics
: asked on 2anymnt

03.04.2022

a. (1/2)x - 5y = 10

(-1/2)x + 5y = -10

b. 7x + 2y = -14

-7x + 2y = -14

c. x + 6y = -18

x - 6y = 18

d. (3/4)x - 9y = 12

(-3/4)x + 9y = 12

1

07.01.2023, solved by verified expert

Unlock the full answer

1 students found this answer helpful

**Answer:**

(-1/2)x + 5y = -10

**Step-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**

Studen helps you with homework in two ways: