SOLUTION: Find the value of m for which the pair of simultaneous equations 3x + my = 5 and (m + 2)x + 5y = m have: a) infinitely many solutions b) no solutions.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Find the value of m for which the pair of simultaneous equations 3x + my = 5 and (m + 2)x + 5y = m have: a) infinitely many solutions b) no solutions.      Log On


   

Question 1015841: Find the value of m for which the pair of simultaneous equations 3x + my = 5 and (m + 2)x + 5y = m have:
a) infinitely many solutions
b) no solutions.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at the coefficient matrix,
A=%28matrix%282%2C2%2C%0D%0A3%2Cm%2C%0D%0Am%2B2%2C5%29%29
The determinant is then,
15-m%28m%2B2%29=15-m%5E2-2m=-m%5E2-2m%2B15
Look for values of m that make the determinant equal to zero,
m%5E2-2m%2B15=0
%28m%2B5%29%28m-3%29=0
So then when m=-5, the equations become,
3x-5y=5
-3x%2B5=-5
and you see that the second equation is just the first equation multiplied by -1.
So this dependent system has infinitely many solutions.
.
.
.
When m=3, the equations become,
3x%2B3y=5 or x%2By=5%2F3
5x%2B5y=3 or x%2By=3%2F5
So the equations are now parallel and therefore have no solution.