What are the solutions to #y = -2x + 2# and #2y = -4x +4#?
Let's start by putting the two equations in the same form-
This can be done by dividing both sides of the first equation by
The two lines have the same equation, hence there are infinite solutions (since the two lines lie one on top of one another). The previous statement can be confirmed by selecting any x point and substituting it into both equations, and getting the same result.
Hopefully this helps!
Infinitely many solutions. See below.
The first thing we need to do in order to classify this system is to solve for
We just have to focus on this one:
We want to get
Our system now looks like this:
Hm...they're the same equation! That means there are infinitely many solutions. An infinite number of points satisfy the system, because every
Protip: Whenever the equations are the same, there will be infinitely many solutions. Whenever the slopes are the same, but the intercepts are different (for example,