Answer:
The system of equations is a consistent system
Step-by-step explanation:
we have
[tex]y=-x+12[/tex] ----> equation A
[tex]y=-2x+2[/tex] ----> equation B
Multiply by [tex]-1[/tex] equation A
[tex]-y=-(-x+12)[/tex] -----> [tex]-y=x-12[/tex] -----> equation C
Adds equation B and equation C
[tex]y=-2x+2\\-y=x-12\\--------\\0=-2x+x+2-12\\0=-x-10\\x=-10[/tex]
Find the value of y
[tex]y=-(-10)+12=22[/tex]
the solution is the point [tex](-10,22)[/tex]
The system has one solution
therefore
The system of equations is a consistent system
