Answer:
Infinite solutions.
Explanation:
First you need to change both into slope intercept form: y = mx + b.
3x + y = 1 in slope intercept form is y = -3x + 1 (subtract 3x from both sides). 2y = 2 - 6x in slope intercept form is y = -3x + 1 (divide both sides by 2). Since both lines are the exact same, there will be an infinite number of solutions when you graph.
If you change both equations into slope intercept form and they're the same line and you're not sure about the answer, go back to the original system of equations that you were given and solve for a variable. To do this, first rewrite the equations to make sure the variables are both on one side. In this case we only need to rewrite 2y = 2 - 6x to be 6x + 2y = 2. Now this is what we have:
3x + y = 1
6x + 2y = 2
Let's try solving for y. Multiply the top by -2. After multiplying, write the new equation below the 2nd one.
This is what your work will look like:
-2(3x + y = 1)
6x + 2y = 2
Here is what your equations will look like after multiplying:
6x + 2y = 2
-6x - 2y = -2
Your next step is to add the two equations together. When you do that, you'll see that everything cancels out, which means you'll end up with 0 = 0 after adding. 0 = 0 means infinite solutions.
Hope this helps!