Question

How do you solve this system of equations `x+ 2y = 3 and 2x + 4y = 6`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the first equation by `color(red)(2)`:

`color(red)(2)(x + 2y) = color(red)(2) xx 3`

`(color(red)(2) xx x) + (color(red)(2) xx 2y) = 6`

`2x + 4y = 6`

Because the first equation is actually the same equation as the second there are an infinite number of solutions for this problem.

Answer 2

There is an infinite count of solutions.

Explanation:

They are both different versions of the same equation

Consider: `2x+4y=6`

All the numbers are even so lets simplify by dividing both sides by 2 giving:

`x+2y=3`

This is now identical to the other equation. Thus one is superimposed on the other (they are coincident)

Thus picking any point on one will also be a point on the other.

Thus there is an infinite count of solutions.