Answer
infinitely many solutions
{(x,y)|y=3x-1}
Work Step by Step
y=3x-1
plug this value for y into the other equation.
x+y-1=2(y-x)
x+(3x-1)-1=2((3x-1)-x)
x+3x-1-1=2(3x)-2(1)-2(x)
x+3x-2=6x-2-2x
4x-2=6x-2x-2
4x-2=4x-2
4x-4x-2=4x-4x-2
-2=-2
Since the variables were eliminated and the statement is true, the system has infinitely many solutions. The solution set is equal to either of the equations, for example {(x,y)|y=3x-1}.
