Question

Solve using the elimination method:

3x+4y=2
6x+8y=4

Answer 1

multiply first equation by -2 and then add
\[-6x-8x=-4\]
\[6x+8x=4\] when you add you get
\[0=0\] because everything drops out. that means they are the same line

Answer 2

it does not mean there is no solution. nor does it mean that you cannot solve it. it means they are the same line, they just look different

Answer 3

so any point on one line is also on the other. there are infinitely many solutions

Answer 4

Satellite is right

Answer 5

in fact before you do anything you see that there is no difference between
\[3x+4y=2\] and \[6x+8y=4\] one is just twice the other on both sides, so any pair that fits one will fit the other

Answer 6

I knew there was infinite solutions, I just didn't think it was solvable using the elimination method

Answer 7

To reliably solve linear systems of equations you should always use row reduction (gaussian elimination)

Answer 8

In this case you can just rearrange the first equation in terms of x and let y be arbitrary. But you would get this result with row reduction.

Answer 9

x = (-4/3)y + 2/3

Answer 10

Where y is any element of the field.