Question

System of equations, special case infinitely many solutions?????

Answer 1

One possible system is

1x + 3y = 4

2x + 6y = 8

Note how 2 is twice as large as 1, 6 is twice as large as 3, and 8 is twice as large as 4.

In other words, the second equation is the result of multiplying both sides of the first equation by 2.

1x+3y = 4

2*(1x+3y) = 2*4

2x+6y = 8

Effectively the two equations in bold are the same which produces the same line. The two lines overlap perfectly to intersect infinitely many times. An intersection is a solution.