Question

Muriel says 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. Which could be the other equation?

Answer 1

Infinite number of solutions...means it will be the same line.
you have probably heard about equivalent fractions like 1/2 = 2/4...and if u reduce 2/4, it equals 1/2. Well...there are also equivalent equations. They can also be reduced.

3y = 2x - 9 cant be reduced, but u can make an equivalent equation by multiplying it all by a number.Any number.

lets try 2...
2(3y = 2x - 9) =
 6y = 4x - 18...this is an equivalent equation....the same line..infinite solutions.Notice that u can reduce it by dividing everything by 2 which would equal 3y = 2x - 9....so u see, it is like equivalent fractions....kind of...lol

or multiply it by 3
3(3y = 2x - 9) =
9y = 6x - 27....this is also equivalent.....so this is an answer as well

and u can multiply it by 4 and get another equivalent equation..or 5, or 6....and so on...

make any sense ?? Just remember, to get the result of infinite solutions, the equations have to be equivalent