Question

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

Answer 1

it's D got it right on edge

Answer 2

The graph is attached.

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=-(1)/(2)x+3...(1)`

`y=(1)/(2)x-1...(2)`

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

`(1)/(2)x-1=-(1)/(2)x+3`

`(1)/(2)x+(1)/(2)x-1=-(1)/(2)x+(1)/(2)x+3`

`(1+1)/(2)x-1=3`

`(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=-(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)`.