How do you determine whether a linear system has one solution, many solutions, or no solution when given 5x+3y=19 and -5x+2y=21?
1 Answer
Oct 14, 2015
#x=-1#
#y=8#
Explanation:
#5x+3y=19#
#-5x+2y=21#
If the two lines are parallel, then they have no solution.
If one equation is a multiple of another equation, then they have many solutions.
#5x+3y=19# ---------------(1) Add the two equations.
#-5x+2y=21# ---------------(2)
#5y=40#
#y=40/5=8#
Substitute
#5x+3(8)=19#
#5x+24=19#
#5x=19-24=-5#
#x=(-5)/5=-1#
