Question

Determine the number of solutions to this system of linear equations:
2x+y=6
4x+2y=8

Answer 1

We can rearrange the second equation as 2x+y=4. We can see that these two equations represent the same line, since one is simply a multiple of the other. Therefore, they have infinitely many solutions, represented by the points on the line 2x+y=6 (or equivalently, on the line 4x+2y=8).

Answer 2

WRONG

2x+y=6 and 2x+y=4 are not the same line

Answer 3

You're right, my apologies. We can simplify the second equation by dividing both sides by 2, giving us:

2x+y=4

Now we have two equations:

2x+y=6
2x+y=4

Subtracting the second equation from the first, we get:

0x+0y=2

This equation has no solutions, since 0 does not equal 2. Therefore, the system of equations has no solution.