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

Accepted Solution

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.[tex]y=-\frac{1}{2}x+3...(1)[/tex][tex]y=\frac{1}{2}x-1...(2)[/tex]First of all, we will find the solution of both equations by equating them as: Β [tex]\frac{1}{2}x-1=-\frac{1}{2}x+3[/tex][tex]\frac{1}{2}x+\frac{1}{2}x-1=-\frac{1}{2}x+\frac{1}{2}x+3[/tex][tex]\frac{1+1}{2}x-1=3[/tex][tex]\frac{2}{2}x-1=3[/tex][tex]x-1=3[/tex][tex]x-1+1=3+1[/tex][tex]x=4[/tex]Upon substituting [tex]x=4[/tex] in equation (1), we will get:[tex]y=-\frac{1}{2}(4)+3[/tex][tex]y=-2+3[/tex][tex]y=1[/tex]Since the solution of our given system is [tex](4,1)[/tex], therefore, the both graphs will intersect at Β [tex](4,1)[/tex].