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 are an infinite number of solutions. The second equation is 4 times the first (8x−16y=32 = 4(2x−4y=8)), so they represent the same line. Equivalently, x−2y=4, so all points (x,y) = (2y+4, y) satisfy the system.