3. Identify the number of solutions to the system of equation:

Question

y=⅓ x + 2
-x +3y = 6

Answer 1

To find the number of solutions to the system of equations, we can first rewrite the second equation in terms of y:

-x + 3y = 6
=> -x = -3y + 6
=> x = 3y - 6

Now, we can substitute this expression for x in the first equation:

y = 1/3(3y - 6) + 2
=> y = y - 2 + 2
=> y = y

From this equation, we can see that the value of y can be any real number. This means that the system of equations has infinite solutions.

Graphically, we can see that the two equations represent two lines that are parallel. Since they never intersect, there are infinite solutions.