Question

A system has an infinite number of solutions. one equation is 3x-3y=8. Which could be the other equation in the system of equations?

Answer 1

`6x-6y-16=0`

Explanation:

Consider the following system of equations:

`a_1x+b_1y+c_1=0\\\\a_2x+b_2y+c_2=0`

The system of equations has infinite solutions if
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

One equation is
`3x-3y=8`

`3x-3y-8=0`

Take another equation as
`6x-6y-16=0`

So, the two equations are
`3x-3y-8=0` and
`6x-6y-16=0`

`a_1=3,b_1=-3,c_1=-8,a_2=6,b_2=-6,c_2=-16`

`(a_1)/(a_2)=(3)/(6)=(1)/(2)\\ (b_1)/(b_2)=(-3)/(-6)=(1)/(2)\\ (c_1)/(c_2)=(-8)/(-16)=(1)/(2)`

So,

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`

Therefore, another equation can be
`6x-6y-16=0`