Muriel sees she has written a system of two linear equations that has an infinite number of solutions one of the equations of the system is 3Y = 2X - 9 what could be the other equation?

Eq2 : 6Y = 4X - 18

Step-by-step explanation:

- For any system of equation to have "infinitely" many solutions then at-least 2 equations must be dependent equations.

- The dependent equations have many solutions as the existence of one makes the other equation redundant,

- In other words, the basic example would be a scalar multiple of original equation.

aY = bX + C ... Eq 1

- The scalar multiple "k", can be any non-zero real value:

kaY = kbX + Ck ... Eq 2

- We divide the two equations:

Eq2 / Eq1 = k ... constant (non-zero)

- Linear independence check invalidates as their exist no non-zero scalar multiple (a, b) such that:

Eq1*a + Eq1*b = 0 ... Hence, equations are dependent

- So choose any value of k = 2:

2*Eq1 : Eq2

Eq2 : 2 * (3Y = 2X - 9)

Eq2 : 6Y = 4X - 18