What is the solution to the following system? 2x + y = 3 4x + 2y = 6

Question

just trying to find out

Answer 1

This system is what they call "indeterminate" -- it actually has an infinite number of solutions.

 

One way to see this is to multiply both sides of the first equation by 2:

 

2x + y = 3

4x + 2y = 6

 

That's the same as the second equation.  In other words, in a sense you really only have one equation, but with two unknowns you need two different equations to come up with a solution.  Any time you have two unknowns, with two equations that are equivalent to each other, you don't have a specific solution.  Any combination of x and y that satisfies one equation also satisfies the other, and there are an infinite number of such x,y pairs.

 

Another way to see it is to graph the two equations.  You'll see that they both fall on the same line -- they don't intersect.  That means that any point on the line satisfies both equations, and there are an infinite number of points on the line.