Question

How many solutions does the system of equations `3x + 7y = 4` and `6x + 14y = 8` have?

Answer 1

This system has infinitely many solutions.

Explanation:

These equations are linearly dependent (second equation is the first equation multiplied by 2). If one of the equations is a multiply of the other, then the system has infinitely many solutions.

Answer 2

There are infinite solutions to this system of equations

Explanation:

Proof:

Pick any solution set that works in the equation 3x + 7y = 4, and you'll see it works in both equations. There is an infinite number of points that will work for this system, so the solution is (x, `-3/7x` - `4/7`)

Here is the graph of a system with infinite solutions.

Hopefully you understand now!