a system of linear equations had infinitely many solutions. does that mean any ordered pair in the coordinate plane is a solution

Question

i need help trying to find the answer to the question i asked . thanks

Answer 1

A system of infinite solutions means that the two (or more) lines given to us lay on top of one another:

y = 6x + 3

2y = 12x + 6

 

If we put 1 in for x, we get 9 out for y, or (1, 9). 2 would give us 15 for y or (2, 15) and so on

 

(3, 6) is a point in the coordinate the plane; is that a solution?

6 = 6 * 3 + 3

6 = 18 + 3

6 ≠ 21

 

So no, not every ordered pair in the plane is a solution to a system of linear equations.