Question

Which statement describes the solution to this system of equations?



{
2
x
−
4
y
=
8
8
x
−
16
y
=
32




There is exactly one solution,
(
2
,
4
)
.


There is exactly one solution,
(
8
,
32
)
.


There is no solution to the system of equations.


There is an infinite number of solutions to the system of equations

Answer 1

There is an infinite number of solutions to the system of equations.

Reason: 8x − 16y = 32 is 4·(2x − 4y = 8), so both equations are the same line. For example, x = 4 + 2y gives infinitely many solutions (e.g. (4,0), (6,1), ...).