Question 59763


The directions state to determine whether the system has one slutions, no solution or infinitely many solutions may you please help

y = -x + 2

3x + 3y = 6

The easiest way to determine this is to put both equations into slope intercept form. {{{highlight(y=mx+b)}}}, where m=slope, and b is the y-intercept.  If their slope (m) is different(even after you reduce) then there is one solution.  The their slope (m) is the same and their y-intercept (b) is different, the lines are parallel and will never intercect, so there is no solution.  If their slopes (m) are the same and the y-intercept (b)is the same they are graphically lying right on top of each other, they share all points and they have infinitely many solutions.
y=-x+2  is already in slope intercept form, m=-1 and b=2
3x+3y=6
-3x+3x+3y=-3x+6
3y=-3x+6
3y/3=-3x/3+6/3
y=-x+2 -->m=-1 and b=2
There are infinitely many solutions.
Happy Calculating!!!