Question

How many solutions does the system of equations `7x + y = 1` and `14x + 2y = 17` have?

Answer 1

No real solutions

Explanation:

Rewrite both equations in slope-intercept form:

For the first equation:

`y=-7x+1`

For the second equation:

`y=-7x+17`

We can see that they have the same slope and different y-intercepts. That means they're parallel lines and never cross.

However, just to be sure, we can set the two equations together and attempt to solve for `x`:

`-7x+1=-7x+17`

Subtract `1` on both sides:

`-7x+1-1=-7x+17-1`

This gives you:

`-7x=-7x+16`

Now move all the `x`s on one side. Add `7x` to both sides.

`-7x=-7x+16+7x`

This gives:

`0=16`

Obviously, this statement is false. That means that the graphs never touch. If the two equal each other, then the graphs will always touch.