Answer:
The solution(s) to a system of equations is the point(s) of intersection.
To find the solution, equate the equations and solve for x to find the x-coordinate:
[tex]\implies f(x)=g(x)[/tex]
[tex]\implies 3x+2=[x-1]+1[/tex]
[tex]\implies 3x+2=x[/tex]
[tex]\implies 2x=-2[/tex]
[tex]\implies x=-1[/tex]
Now substitute the value of x into one of the equations to find the y-coordinate of the solution:
[tex]f(-1)=3(-1)+2=-1[/tex]
So the solution to this system of equations is (-1, -1)
Therefore, (1, 5) is NOT a solution to the system of equations.
Let's check
[tex]\\ \rm\rightarrowtail y=3x+2[/tex]
[tex]\\ \rm\rightarrowtail 5=3+2[/tex]
[tex]\\ \rm\rightarrowtail 5=5[/tex]
Verified
And
[tex]\\ \rm\rightarrowtail y=[x-1]+1[/tex]
[tex]\\ \rm\rightarrowtail 5=1-1+1[/tex]
[tex]\\ \rm\rightarrowtail 5\neq 1[/tex]
No
