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