Question

Which graph represents the solution set to this system of equations? Y=-1/2x+3 and y= 1/2x-1

Answer 1

Hey there, I hope I can be of assistance today!
While there are no graphs, I can provide you with the graph to answer your question assuming you have choices of graphs!

Hope this helps!

Answer 2

Answer:

The graph is attached.

Step-by-step explanation:

We have been given a system of two equations. We are asked to find the graph that represents the solution set to this system of equations.

$y=-\frac{1}{2}x+3...(1)$

$y=\frac{1}{2}x-1...(2)$

First of all, we will find the solution of both equations by equating them as:  

$\frac{1}{2}x-1=-\frac{1}{2}x+3$

$\frac{1}{2}x+\frac{1}{2}x-1=-\frac{1}{2}x+\frac{1}{2}x+3$

$\frac{1+1}{2}x-1=3$

$\frac{2}{2}x-1=3$

$x-1=3$

$x-1+1=3+1$

$x=4$

Upon substituting $x=4$ in equation (1), we will get:

$y=-\frac{1}{2}(4)+3$

$y=-2+3$

$y=1$

Since the solution of our given system is $(4,1)$, therefore, the both graphs will intersect at  $(4,1)$.