Answer:
We are asked to find which graph represents the solution of the given system of equations:
[tex]y=-x+2------------(1)[/tex]
and [tex]y=3x-1-------------(2)[/tex]
We find the intersection point of the two equations by solving these system of equations using elimination method as:
subtract equation (2) from equation (1) to obtain:
[tex]0=-4x+3[/tex]
[tex]3=4x[/tex]
[tex]x=\dfrac{3}{4}=0.75[/tex]
Also putting this value of x in equation (1) we get:
[tex]y=-\dfrac{3}{4}+2\\\\y=\dfrac{-3+4\times 2}{4}\\\\y=\dfrac{-3+8}{4}\\\\y=\dfrac{5}{4}=1.25[/tex]
Hence, the intersection point is: (0.75,1.25).
Hence the graph that represents the solution of the system of given linear equations is attached to the answer.
