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
Nallasivam V
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 y=8 in equation (1)

5x+3(8)=19
5x+24=19
5x=19-24=-5
x=(-5)/5=-1

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