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.

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) (Show Source): You can put this solution on YOUR website!
Let's look at the coefficient matrix,

The determinant is then,

Look for values of that make the determinant equal to zero,

So then when , the equations become,

and you see that the second equation is just the first equation multiplied by .
So this dependent system has infinitely many solutions.
.
.
.
When , the equations become,
or
or
So the equations are now parallel and therefore have no solution.

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