Answer:
[tex]\text\large\boxed{\text{Quadrant 4}}\large\boxed[/tex]
Step-by-step explanation:
We can solve this using a simple systems of equations.
First: set both equations equal to each other.
[tex]y = -3x + 1[/tex]
[tex]y = 6x - 3[/tex]
These can be set as equal functions since both contain the term "y = something."
[tex]6x - 3 = -3x + 1[/tex]
Now, solve for x.
- Add 3x to both sides: [tex]9x - 3 = 1[/tex]
- Add 3 to both sides: [tex]9x = 4[/tex]
- Divide both sides by 9: [tex]x = \frac{4}{9}[/tex]
Use the value of x to solve for y.
We can plug it into one of our equations and solve for y.
- [tex]y=-3(\frac{4}{9})+1[/tex]
- [tex]y = -\frac{12}{9} + 1[/tex]
- [tex]y = -\frac{12}{9} + \frac{9}{9}[/tex]
- [tex]y = -\frac{3}{9}[/tex]
- [tex]y = -\frac{1}{3}[/tex]
Get our final coordinate and determine the Quadrant
Now that we have x and y, we can determine that our final coordinate of the point of intersection is [tex](\frac{4}{9}, -\frac{1}{3})[/tex].
- A positive x and a negative y corresponds to Quadrant 4. Thus, this point of intersection is located in QUADRANT 4.
Hope this helped!
